Notes from the bulk

Erica Bertolini

REVIEW 3 major objections 3 minor 261 references

Notes from the bulk

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Pith's one-line read This thesis derives local, time- and position-dependent edge velocities in Hall systems from curved-bulk Chern-Simons and BF theories, and extends nontrivial boundary dynamics with Kac-Moody algebras to Maxwell, fracton, and…

desk verdict Real algebraic content, especially the linearized-gravity Kac-Moody algebra, but the curved-metric explanation of accelerated edge modes is a free-parameter relabeling, not a prediction. read the letter →

arxiv 2507.16744 v1 pith:HJBATQD6 submitted 2025-07-22 hep-th cond-mat.mes-hallcond-mat.str-elgr-qc

Erica Bertolini This is my paper

classification hep-thcond-mat.mes-hallcond-mat.str-elgr-qc

keywords Chern-SimonstheoryBFedgemodesKac-MoodyalgebrasfractonslinearizedgravityquantumHalleffectbulk-boundarycorrespondence

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The thesis argues that the boundary physics of topological quantum field theories is not fixed by the flat-space paradigm: if Chern-Simons and BF theories are placed on a curved bulk with a radial boundary, the chiral edge modes of Hall systems acquire local velocities that depend on time and position along the edge. The induced metric enters the boundary action only through its determinant, and the holographic contact between bulk boundary conditions and boundary equations of motion ties the edge velocity to a boundary action parameter, so a curved bulk metric acts as a field-theoretic replacement for the ad hoc potentials used in phenomenological models. The thesis further argues that nontrivial boundary dynamics is not restricted to topological theories: Maxwell theory, a newly built covariant theory of fractons (quasiparticles with restricted mobility), and linearized gravity with boundary all display conserved edge currents forming Kac-Moody algebras. If correct, this supplies a framework for accelerated edge modes in Hall systems, predicts accelerated edge modes in topological insulators, and connects fracton and gravitational boundary states to condensed-matter edge physics.

What carries the argument

The load-bearing mechanism is the holographic contact in the bulk-to-boundary correspondence. Starting from a symmetry, one writes the invariant bulk action on a manifold with a one-sided boundary introduced by a $\theta$ function, adds the most general boundary term allowed by locality and power counting, derives the boundary conditions and the broken Ward identity, extracts the conserved edge currents and their Kac-Moody algebra, and identifies the boundary degrees of freedom as scalars. The decisive step is matching the bulk boundary conditions with the equations of motion of the induced lower-dimensional action; this holographic contact fixes the free parameters of the boundary theory. In curved spacetime it gives $v = a_2/\tilde\kappa$ with $\tilde\kappa = \kappa \tilde\epsilon^{012}/\sqrt{-g}$, so the metric determinant becomes an observable input and the edge velocity becomes local. For the non-topological half of the thesis, the same machinery runs on the broken Ward identities produced by the boundary, yielding Kac-Moody algebras for Maxwell, fracton, and linearized-gravity theories.

What would settle it

Measure the local edge velocity of a fractional quantum Hall system on a deliberately curved or strained sample and check whether it follows the profile predicted by the determinant of an induced metric through $v = a_2/\tilde\kappa$; if no single choice of boundary coefficients reproduces the observed $v(t,\theta)$, the claimed correspondence fails.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the edge velocity of the chiral bosons living on the boundary of abelian Chern-Simons and BF theories becomes a local function when the bulk manifold is curved: $v = v(t,\theta)$ rather than a constant. The mechanism is a bulk-to-boundary correspondence: adding a radial boundary to a three-dimensional topological theory, working in Gaussian normal coordinates, and requiring compatibility between the bulk boundary conditions and the equations of motion of the induced two-dimensional action yields the holographic contact $v = a_2/\tilde\kappa$, where $\tilde\kappa = \kappa \tilde\epsilon^{012}/\sqrt{-g}$ is a scalar built from the Chern-Simons level and the metric determinant. The metric dependence survives only through the determinant, which is why the effect is mild yet sufficient to make edge modes accelerate. The thesis also establishes that the Kac-Moody algebra on the edge and its central charge $1/\kappa$ are metric-independent, so topological protection remains while the velocity becomes dynamical. Beyond topological theories, the same boundary formalism applied to Maxwell theory, to a new covariant fracton gauge theory built from the symmetry $\delta A_{\mu\nu} = \partial_\mu\partial_\nu\Lambda$, and to linearized gravity yields conserved boundary currents with Kac-Moody algebras, generalized in the fracton case and standard in the linearized-gravity case.

Load-bearing premise

The load-bearing premise is that a curved bulk metric with a radial boundary can faithfully encode the physical confining potential of a real Hall sample, while the edge velocity $v$ is treated as a free experimental input; the thesis gives no rule for deriving the metric from the sample's potential or microscopic interactions.

Editorial extensions

If this is right

Observed accelerated chiral edge modes in Hall systems can be described without adding ad hoc potentials: a curved bulk metric supplies the local velocity through the determinant of the induced metric.
The Kac-Moody algebra on the edge and its central charge remain the protected structures of the flat case, separating topological algebraic data from unprotected local dynamics.
Topological insulators described by BF theory with a time-reversal-invariant boundary term should exhibit equal-and-opposite but locally varying edge velocities; the thesis predicts accelerated edge modes in these systems.
Boundary dynamics is not exclusive to topological theories: Maxwell theory, a new covariant theory of fractons, and linearized gravity each display conserved edge currents forming Kac-Moody algebras.
The new covariant fracton gauge theory recovers standard fracton features, including multipole conservation and Maxwell-like equations, and its boundary dynamics may be related to higher-order topological insulators.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: if the metric-to-potential correspondence holds, the local edge velocity could be used in reverse as a probe that reconstructs the bulk metric determinant from edge transport data; the thesis itself treats the metric as input rather than output.
Editorial inference: the same curved-boundary mechanism might apply to engineered curved or strained Hall samples, suggesting testable accelerated edge modes beyond the geometries explicitly treated in the thesis.
Editorial inference: the generalized Kac-Moody algebra on the fracton boundary hints at an algebraic classification of higher-order topological insulators in terms of multipole-conservation data, a connection the thesis notes but does not develop into a classification.
Editorial inference: a standard Kac-Moody algebra on the boundary of linearized gravity may offer a minimal holographic template for spin-2 theories outside anti-de Sitter holography; this is a speculation beyond the thesis's own claims.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: the original technical content of this thesis is already in seven published papers, so what is new here is the packaging and the narrative. That is not a flaw; the derivations are written out carefully and are internally consistent. The most valuable pieces are the boundary Kac-Moody algebra for linearized gravity, which had been suspected but not proven, and the covariant fracton gauge theory. Those are real contributions and I would point a student to them.

The soft spot is the advertised physical result. Chapter 5 claims that a curved bulk metric explains accelerated Hall edge modes and predicts local modes in topological insulators. Reading Section 5.1.3, the velocity v starts as a free coefficient in the boundary action and is then tied to the metric determinant by v = a2/kappa-tilde. Because a2 is free and the bulk metric is not determined by any physical input, the relation is a relabeling: any local positive v(t,theta) can be produced by choosing a metric with the right determinant and tuning a2. The thesis itself states that v must be fixed by experimental inputs. So the curved metric is not explaining the acceleration; it is a dictionary for encoding a phenomenological velocity. There is no equation mapping a physical confining potential or microscopic interaction to the bulk metric, and without that the topological insulator prediction is not falsifiable. The stress-test note is correct.

The BF section has the same structure but also contains the best physics: the time-reversal analysis selects equal-and-opposite local velocities, which is a genuine classification result for possible TI edge states. Still, those velocities depend on free boundary parameters and on the metric, so it remains a framework that permits local velocities rather than a derivation of them.

Who should read this: graduate students learning Symanzik-style boundary QFT, and people working on boundary current algebras for non-topological theories. I would not cite the thesis itself; I would cite the underlying published papers. If this were submitted as a research article, I would not let the central claim pass as stated. But the formal core is substantial enough that I would send it to referees rather than desk-reject, with the clear instruction that the predictive claim in Chapter 5 has to be reframed or supported by an actual metric-to-potential map.

Referee Report

3 major / 3 minor

Summary. This thesis develops a QFT framework for boundary effects, following Symanzik, and applies it to topological Chern-Simons and BF theories on curved backgrounds and to non-topological Maxwell, fracton, and linearized-gravity theories. The central physical claim is that edge chiral bosons of Hall systems acquire local, time- and position-dependent velocities when the bulk TQFT lives on a curved spacetime: the induced boundary metric determinant enters the edge action through the holographic contact v = a2/kappa-tilde, and this is proposed as an alternative to adding an ad hoc local potential to the Luttinger model. The thesis also derives Kac-Moody current algebras on the boundaries of Maxwell theory, a covariant fracton model, and a Kac-Moody algebra for linearized gravity.

Significance. The detailed formal derivations are a strength: broken Ward identities, boundary conditions, equal-time commutators, canonical identification, and holographic contacts are written out, and the positivity of the Kac-Moody central charge is used to fix the sign of the bulk coupling. If the central claim were established, it would provide a field-theoretic encoding of accelerated edge modes and broaden the boundary paradigm beyond TQFTs. However, the central claim is not currently predictive: Section 5.1.3 states that v must be fixed by experiment, a2 is a free function of the determinant, and no equation maps a physical confining potential or microscopic interaction to the bulk metric. The curved metric therefore reparameterizes the free velocity rather than explaining it. The formal results remain valuable, but the advertised physical interpretation needs to be substantially reframed or supplemented.

major comments (3)

[5.1.3 (Eq. 5.1.71)] The central claim that a curved bulk metric produces accelerated edge modes is not supported as a prediction. The holographic contact (5.1.71) reads v = a2/kappa-tilde, where a2 is a free parameter depending at most on the metric determinant (5.1.67) and kappa-tilde is given in terms of sqrt(-g) (5.1.16). The manuscript explicitly states in Section 5.1.3 that v 'must be determined by experimental inputs.' Since both a2 and the bulk metric are unconstrained by any independent dynamics, any sufficiently regular local velocity profile can be reproduced by choosing the metric determinant and tuning a2; the metric does not constrain v, it only relabels it. The proposed alternative to the ad hoc Luttinger potential therefore requires a derivation of the bulk metric from the sample's confining potential or interactions, which Section 5.1.4 does not supply.
[5.2.3 and 5.2.5 (Eqs. 5.2.99, 5.2.102)] The BF generalization inherits the same underdetermination. The velocities v_+ and v_- given by (5.2.99) and (5.2.102) are functions of the boundary coefficients l_i and c_hat_22; these are free parameters of the boundary action (5.2.5) and are not fixed by the bulk theory. Section 5.2.5 then predicts accelerated edge modes in topological insulators, but every observed velocity profile can be matched by choosing the boundary coefficients and a metric. Without an independent criterion selecting the metric or the l_i, the prediction is not falsifiable. The positivity and time-reversal arguments constrain the signs and equality of v_+ and v_-, but not their local spacetime dependence.
[5.1.4] The interpretive claim that 'a change of potential can be effectively encoded in the Chern-Simons theory by a bulk metric' is an assertion, not a derived statement. The bulk metric is a non-dynamical background; the only derived relation is through the determinant of the induced metric, and no equation connects that determinant to a microscopic potential. This is not an algebraic inconsistency, but it means the word 'explanation' in the abstract and Chapter 5 overstates what the holographic contact establishes. The authors should either supply such a map or explicitly reframe the result as a formal encoding in which arbitrary local velocities can be accommodated.

minor comments (3)

[5.1.1, footnote] The abbreviation 'GNG' in the footnote on Gaussian normal coordinates should read 'GNC'.
[5.1.4] The word 'holografic' should be corrected to 'holographic'.
[5.2.4] The list of boundary conditions at r = 0 in (5.2.24) is stated without derivation; adding a short justification would improve readability.

Circularity Check

2 steps flagged · score 6.0 of 10

The claimed prediction of accelerated edge modes reduces by construction: the chiral velocity is declared a free phenomenological input and then rewritten through the holographic contact as a metric-dependent boundary coefficient.

fitted input called prediction [Section 5.1.3, Eqs. (5.1.67) and (5.1.71)]
"The fact that v is a phenomenological parameter requires that it should be determined by experimental inputs ... v = a2/κ̃ ... a2 is a free parameter depending at most on the metric determinant: a2 = a2(γ)."

The holographic contact (5.1.71) defines v as a2/κ̃, where a2 is explicitly a free boundary coefficient of the action (5.1.68) and κ̃ is determined by the metric determinant. Since the bulk metric is not dynamical and no equation maps a physical confining potential to the metric, any local function v(t,θ) can be represented by choosing a2 and the metric determinant accordingly. The paper itself states that v must be fixed by experimental inputs, so the 'curved bulk produces accelerated edge modes' result is a relabeling of the assumed local velocity rather than a prediction from the bulk theory.
self definitional [Section 5.2.3, Eqs. (5.2.93)-(5.2.99), and Section 5.2.4]
"As a consequence of the holographic contact, the metric dependence of the boundary parameters (5.2.80) is transferred to the li coefficients through (5.2.93) and (5.2.94). This makes v± depend on the determinant of the induced metric v± = v±(γ). We therefore remark the crucial point that the fact of dealing with a curved bulk spacetime has the primary consequence that the velocities of the edge modes depend on both time and space v± = v±(t, θ), differently to what happens for flat backgrounds."

In the BF construction the local velocities v± are functions of the free boundary coefficients li and ĉ22 of Sbd (5.2.5) and of the 2D action (5.2.82). The 'metric dependence' is introduced by allowing those coefficients to depend on the induced metric determinant; no bulk dynamics or microscopic input fixes them. Hence the statement that a curved bulk implies local, accelerated edge modes is equivalent to the ansatz that the boundary coefficients, and therefore v±, are local functions of γ. The claimed prediction for Topological Insulators is a restatement of this chosen parametrization, not a consequence forced by the theory.

full rationale

The thesis contains a legitimate field-theoretic derivation: from a Chern-Simons or BF action with a radial boundary, the broken Ward identity, the Kac-Moody algebra, and the induced 2D action are obtained in a self-contained way, and the central charge positivity argument is independent of the curved-background claims. However, the advertised physical payoff - accelerated and position-dependent edge velocities, and the prediction of local modes for Topological Insulators - is not an output of the formalism. In the Chern-Simons case, the velocity is introduced through the free boundary coefficient a2 and then related to the metric determinant by the holographic contact v = a2/κ̃; the paper explicitly says v is a phenomenological parameter to be fixed by experiment. In the BF case, the local velocities v± are written in terms of the unconstrained boundary coefficients li and ĉ22, whose metric dependence is an input. Thus any local velocity profile can be accommodated by choosing the boundary parameters and the metric determinant, and no equation connects the bulk metric to an actual physical confining potential. The observed accelerated edge modes are therefore encoded, not explained; the central 'prediction' reduces by construction to the assumed locality of free parameters. The non-circular parts - the algebraic structure, the central charge, and the constraint that same-direction movers are ruled out by Hamiltonian positivity - are independent results and are not affected by this criticism.

Assumptions & free parameters 7 free parameters · 6 assumptions · 2 invented entities

The boundary physics depends on a large set of free coefficients in the Symanzik boundary terms, and the advertised edge velocities are related to those coefficients plus the metric determinant. The central derivations also assume the Symanzik boundary principle, the radial/axial gauge choices, the scalar solution of the conserved-current equation, positivity selections, and the covariant fracton symmetry. These are reasonable domain assumptions for this program, but they are assumptions rather than derived facts.

free parameters (7)

edge velocity v in Chern-Simons boundary theory = unspecified; set by experimental input
Section 5.1.3 calls v a phenomenological parameter; it enters the boundary condition (5.1.17) and is related to a2 by (5.1.71).
2D boundary coefficient a2(gamma) = free function of the metric determinant
Appears in the action (5.1.68); it is not fixed by symmetry or by the holographic contact.
Chern-Simons boundary term coefficients c1, c2, c3 = free, constrained only by existence of nontrivial boundary conditions
Define the matrix M_ij and hence v through Eqs. (5.1.14)-(5.1.20).
BF boundary coefficients alpha_ij, beta_ij, zeta_ij and l1, l2, l3 = free, constrained by det Lambda = 0 and by time-reversal or positivity
Enter the boundary term (5.2.5) and the boundary condition solutions (5.2.18)-(5.2.20).
BF decoupling coefficient c_hat_22 = set to 0 for time-reversal-symmetric topological insulators, nonzero otherwise
Controls whether the 2D action decouples into Luttinger modes and which physical edge case is realized, Eqs. (5.2.99)-(5.2.117).
Maxwell boundary coefficients a_ab, b_abc, c_ab and central charge combination mu sigma - nu rho = free constants
Enter the boundary term (6.6) and the Kac-Moody central charge (6.19).
fracton and linearized-gravity couplings g1 and g2 = g2 = 0 selects the pure fracton sector
The invariant action is a linear combination, Eq. (7.2.7); the fracton theory is obtained by setting g2 to zero.

assumptions (6)

domain assumption A boundary is implemented by a Heaviside theta in the action, and the most general boundary term compatible with locality and power counting yields the physical boundary conditions.
Used throughout, e.g., Eq. (2.1.14) and Eq. (5.1.9); this Symanzik-style principle restricts the possible boundary physics.
standard math Gauge-fixing choices (axial or radial) and Gaussian normal coordinates do not affect the physical boundary results.
Invoked in Sections 4.1, 5.1.1, and 5.2.1 to compute in convenient gauges; standard for abelian theories but not proved in the thesis.
standard math The solution of the on-shell conserved current equation is A_i = partial_i Phi + delta_i2 C, with C = 0 by the mean value theorem.
Used to identify boundary scalar degrees of freedom, Eqs. (5.1.29) and (5.2.30)-(5.2.31).
domain assumption Positivity of the Kac-Moody central charge and lower-boundedness of the boundary Hamiltonian select physical parameter ranges.
Gives kappa > 0 and rules out same-direction edge modes, Sections 5.1.1 and 5.2.3.
domain assumption The covariant fracton symmetry delta A_mu_nu = partial_mu partial_nu Lambda is the correct field-theoretic encoding of fracton restricted mobility.
Foundation of Chapter 7; the theory is built from this symmetry rather than from the lattice models.
domain assumption The 2D boundary action is constrained only by power counting, locality, shift symmetry, and canonical-variable matching partial L / partial q_dot = p.
Used to derive the most general boundary actions, e.g., (5.1.53)-(5.1.68); excludes boundary terms that could change the algebra.

invented entities (2)

accelerated chiral edge modes in topological insulators and quantum spin Hall systems
purpose: Predicted observable consequence of a curved bulk metric in BF theory, generalizing constant-velocity helical Luttinger liquids.
Section 5.2.5 explicitly states that generalized topological insulators with accelerated chiral edge modes have not been discovered yet; the thesis offers a theoretical framework but no independent observation.
covariant fracton field strength F_mu_nu_rho built from a symmetric rank-2 field with delta A_mu_nu = partial_mu partial_nu Lambda
purpose: New building block of the covariant fracton Maxwell theory; it recovers Gauss constraints and mobility restrictions from equations of motion.
Introduced in Section 7.2 as a new tensor; no independent experimental handle is provided, and it is a theoretical construct.

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Cite this review

Pith. "Pith review of Notes from the bulk." pith.science (2026). https://pith.science/paper/HJBATQD6

@misc{pith2026250716744,
  author       = {Pith},
  title        = {Pith review of: Notes from the bulk},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HJBATQD6}},
  note         = {Machine review of arXiv:2507.16744}
}

read the original abstract

The scope of this Ph.D thesis is to study the effects of the presence of a boundary from a Quantum Field Theoretical perspective, searching for new physics and explanations of observed phenomena. In particular, thanks to the formal QFT setting, the issue of the existence of local, accelerated, edge modes in Hall systems is analyzed and understood in terms of the bulk-to-boundary approach as related to a curved background in topological QFTs with boundary. Within this formalism the induced metric on the boundary can be associated to the ad hoc potential introduced in the phenomenological models in order to obtain such non-constant edge velocities. This also leads to the prediction of local modes for Topological Insulators, and Quantum Spin Hall systems in general. The paradigm for which only topological QFTs have a physical content on the boundary is broken, and also non-Topological Quantum Field Theories such as fracton models and Linearized Gravity are shown to have non-trivial boundary dynamics. Indeed due to the breaking of their defining symmetry both models have a current algebra of the Kac-Moody type on the boundary. In the case of fractons this algebra is in a generalized form, which also appears in some kinds of higher order Topological Insulators, a sign of a possible relation between these materials and edge states of fracton quasiparticles. Concerning the theory of Linearized Gravity, instead, the algebra is a standard Kac-Moody one, whose presence was suspected, but never proved before. Physical results on the boundary range between condensed matter, elasticity and (massive) gravity models. A collateral result, which enrich this Thesis, is the building of a new covariant QFT for fractons with a peculiar gauge structure. This new model better highlight the properties of these quasiparticles.

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Works this paper leans on

261 extracted references · 33 canonical work pages

[1]

«Holographic Projection of Electro- magnetic Maxwell Theory»

Erica Bertolini and Nicola Maggiore. «Holographic Projection of Electro- magnetic Maxwell Theory». Symmetry 12.7 (2020), p. 1134. doi: 10 . 3390 / sym12071134. arXiv:2006.14902 [hep-th]

arXiv 2020
[2]

«Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory».Phys

Erica Bertolini, Giulio Gambuti, and Nicola Maggiore. «Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory».Phys. Rev. D 104.10 (2021), p. 105011.doi: 10 . 1103 / PhysRevD . 104 . 105011. arXiv: 2110 . 13203 [hep-th]

2021
[3]

675.doi: 10

EricaBertolini,FilippoFecit,andNicolaMaggiore.«TopologicalBFDescription of 2D Accelerated Chiral Edge Modes».Symmetry 14.4 (2022), p. 675.doi: 10. 3390/sym14040675. arXiv:2203.13520 [hep-th]

arXiv 2022
[4]

«Maxwell theory of fractons».Phys

Erica Bertolini and Nicola Maggiore. «Maxwell theory of fractons».Phys. Rev. D 106.12 (2022), p. 125008.doi: 10.1103/PhysRevD.106.125008 . arXiv:2209. 01485 [hep-th]

doi:10.1103/physrevd.106.125008 2022
[5]

«Gaug- ing Fractons and Linearized Gravity».Symmetry 15.4 (2023), p

Erica Bertolini, Alberto Blasi, Andrea Damonte, and Nicola Maggiore. «Gaug- ing Fractons and Linearized Gravity».Symmetry 15.4 (2023), p. 945.doi: 10 . 3390/sym15040945. arXiv:2304.10789 [hep-th]

arXiv 2023
[6]

EricaBertolini,NicolaMaggiore,andGiandomenicoPalumbo.«Covariantfrac- ton gauge theory with boundary».Phys. Rev. D108.2 (2023), p. 025009.doi: 10.1103/PhysRevD.108.025009. arXiv:2306.13883 [hep-th]

arXiv 2023
[7]

«Theory of a symmetric tensor field with boundary: Kac-Moody algebras in linearized gravity».Phys

Erica Bertolini and Nicola Maggiore. «Theory of a symmetric tensor field with boundary: Kac-Moody algebras in linearized gravity».Phys. Rev. D 108.10 (2023), p. 105012.doi: 10 . 1103 / PhysRevD . 108 . 105012. arXiv: 2310 . 20303 [hep-th]

2023
[8]

H. B. G. Casimir. «On the attraction between two perfectly conducting plates». Indag. Math.10.4 (1948), pp. 261–263

1948

Show all 261 references

[9]

S. K. Lamoreaux. «Demonstration of the Casimir force in the 0.6 to 6 microm- eters range».Phys. Rev. Lett.78 (1997). [Erratum: Phys.Rev.Lett. 81, 5475–5476 (1998)], pp. 5–8.doi: 10.1103/PhysRevLett.78.5

1997 doi
[10]

Symanzik

K. Symanzik. «Schrodinger Representation and Casimir Effect in Renormaliz- able Quantum Field Theory».Nucl. Phys. B190 (1981), pp. 1–44.doi: 10.1016/ 0550-3213(81)90482-X

1981
[11]

«Symanzik’s Method Applied To The Fractional Quantum Hall Edge States»

AlbertoBlasi,DarioFerraro,NicolaMaggiore,NicodemoMagnoli,andMaura Sassetti. «Symanzik’s Method Applied To The Fractional Quantum Hall Edge States». Annalen Phys.17 (2008), pp. 885–896.doi: 10.1002/andp.200810323 . arXiv: 0804.0164 [hep-th]

2008 arXiv
[12]

«3+1D Massless Weyl spinors from bosonic scalar-tensor duality»

AndreaAmoretti,AlessandroBraggio,GiacomoCaruso,NicolaMaggiore,and Nicodemo Magnoli. «3+1D Massless Weyl spinors from bosonic scalar-tensor duality». Adv. High Energy Phys.2014 (2014), p. 635286.doi: 10 . 1155 / 2014 / 635286. arXiv:1308.6674 [hep-th]. 171 172 bibliography

2014 arXiv
[13]

«Duality and Dimensional Reduction of 5D BF Theory»

Andrea Amoretti, Alberto Blasi, Giacomo Caruso, Nicola Maggiore, and Nicodemo Magnoli. «Duality and Dimensional Reduction of 5D BF Theory». Eur. Phys. J. C73.6 (2013), p. 2461.doi: 10 . 1140 / epjc / s10052 - 013 - 2461 - 3. arXiv: 1301.3688 [hep-th]

2013 arXiv
[14]

«Topological field theory».Phys

Danny Birmingham, Matthias Blau, Mark Rakowski, and George Thompson. «Topological field theory».Phys. Rept.209 (1991), pp. 129–340.doi: 10.1016/ 0370-1573(91)90117-5

1991
[15]

Moore and Nathan Seiberg

Gregory W. Moore and Nathan Seiberg. «Taming the Conformal Zoo».Phys. Lett. B220 (1989), pp. 422–430.doi: 10.1016/0370-2693(89)90897-6

1989 doi
[16]

Xiao-GangWen.«TheoryoftheedgestatesinfractionalquantumHalleffects». Int. J. Mod. Phys. B6 (1992), pp. 1711–1762.doi: 10.1142/S0217979292000840

1992 doi
[17]

«Edge Waves in the Quantum Hall Effect».Annals Phys.207 (1991), pp

Michael Stone. «Edge Waves in the Quantum Hall Effect».Annals Phys.207 (1991), pp. 38–52.doi: 10.1016/0003-4916(91)90177-A

1991 doi
[18]

Frohlich, Ali H

J. Frohlich, Ali H. Chamseddine, F. Gabbiani, T. Kerler, C. King, P. A. Marche- tti, U. M. Studer, and E. Thiran. «The Fractional quantum Hall effect, Chern- Simons theory, and integral lattices» (Sept. 1994)

1994
[19]

«Physical principles underlying the quantum Hall effect».Comptes Rendus Physique12 (2011), pp

Samuel Bieri and Jurg Frohlich. «Physical principles underlying the quantum Hall effect».Comptes Rendus Physique12 (2011), pp. 332–346.doi: 10.1016/j. crhy.2011.02.001. arXiv:1006.0457 [cond-mat.mes-hall]

2011 arXiv
[20]

«Chiral Anomaly, Topological Field Theory, and Novel States of Matter»

Jürg Fröhlich. «Chiral Anomaly, Topological Field Theory, and Novel States of Matter». Rev. Math. Phys. 30.06 (2018), p. 1840007. doi: 10 . 1142 / 9789813233867_0013. arXiv:1802.01385 [cond-mat.mes-hall]

2018 arXiv
[21]

M. Z. Hasan and C. L. Kane. «Topological Insulators». Rev. Mod. Phys. 82 (2010), p. 3045. doi: 10 . 1103 / RevModPhys . 82 . 3045 . arXiv: 1002 . 3895 [cond-mat.mes-hall]

2010
[22]

«Topological insulators and supercon- ductors».Rev.Mod.Phys

Xiao Liang Qi and Shou Cheng Zhang. «Topological insulators and supercon- ductors».Rev.Mod.Phys. 83.4(2011),pp.1057–1110. doi: 10.1103/RevModPhys. 83.1057. arXiv:1008.2026 [cond-mat.mes-hall]

2011 arXiv
[23]

Zahid Hasan and Joel E

M. Zahid Hasan and Joel E. Moore. «Three-Dimensional Topological Insula- tors». Ann. Rev. Condensed Matter Phys.2 (2011), pp. 55–78. doi: 10 . 1146 / annurev-conmatphys-062910-140432. arXiv:1011.5462 [cond-mat.str-el]

2011 arXiv
[24]

Gregory W. Moore. «The birth of topological insulators».Nature 464 (2010), pp. 194–198.doi: 10.1038/nature08916

2010 doi
[25]

«The Chern-Simons-Landau-Ginzburg theory of the frac- tional quantum Hall effect».Int

Shou-Cheng Zhang. «The Chern-Simons-Landau-Ginzburg theory of the frac- tional quantum Hall effect».Int. J. Mod. Phys. B6 (1992), pp. 25–58.doi: 10 . 1142/S0217979292000037

1992
[26]

Funct.Anal.Appl

V.G.Kac.«Simplegradedalgebrasoffinitegrowth». Funct.Anal.Appl. 1(1967), p. 328

1967
[27]

R.V.Moody.«LieAlgebrasassociatedwithgeneralizedCartanmatrices». Bull. Am. Math. Soc.73 (1967), pp. 217–221.doi: 10.1090/S0002-9904-1967-11688- 4. bibliography 173

1967 doi
[28]

Blasi and R

A. Blasi and R. Collina. «Chern-Simons and two-dimensional conformal field theories in a covariant Lagrangian approach».Phys. Lett. B243 (1990), pp. 99–

1990
[29]

«Chern-Simons theory in the axial gauge: Manifold with boundary».Helv

Stephane Emery and Olivier Piguet. «Chern-Simons theory in the axial gauge: Manifold with boundary».Helv. Phys. Acta64 (1991), pp. 1256–1270

1991
[30]

A. P. Balachandran, G. Bimonte, K. S. Gupta, and A. Stern. «Conformal edge currentsinChern-Simonstheories». Int.J.Mod.Phys.A 7(1992),pp.4655–4670. doi: 10.1142/S0217751X92002106. arXiv:hep-th/9110072

1992 arXiv
[31]

Com- mun

GaryT.Horowitz.«ExactlySolubleDiffeomorphismInvariantTheories». Com- mun. Math. Phys.125 (1989), p. 417.doi: 10.1007/BF01218410

1989 doi
[32]

Karlhede and M

A. Karlhede and M. Rocek. «Topological Quantum Field Theories in Arbitrary Dimensions». Phys. Lett. B224 (1989), pp. 58–60.doi: 10.1016/0370-2693(89) 91050-2

1989 doi
[33]

«Noncommutative two dimensional BF model».Nucl

Alberto Blasi, Nicola Maggiore, and Michele Montobbio. «Noncommutative two dimensional BF model».Nucl. Phys. B740 (2006), pp. 281–296.doi: 10 . 1016/j.nuclphysb.2006.01.028. arXiv:hep-th/0512006

2006 arXiv
[34]

Gil Young Cho and Joel E. Moore. «Topological BF field theory description of topological insulators».Annals Phys.326 (2011), pp. 1515–1535.doi: 10.1016/ j.aop.2010.12.011. arXiv:1011.3485 [cond-mat.str-el]

2011 arXiv
[35]

A.P.BalachandranandP.Teotonio-Sobrinho.«TheEdgestatesoftheBFsystem and the London equations».Int. J. Mod. Phys. A8 (1993), pp. 723–752.doi: 10. 1142/S0217751X9300028X. arXiv:hep-th/9205116

1993 arXiv
[36]

«Bulk-boundary correspondence in (3+1)-dimensional topological phases».Phys

Xiao Chen, Apoorv Tiwari, and Shinsei Ryu. «Bulk-boundary correspondence in (3+1)-dimensional topological phases».Phys. Rev. B94.4 (2016). [Adden- dum: Phys.Rev.B 94, 079903 (2016)], p. 045113.doi: 10 . 1103 / PhysRevB . 94 . 045113. arXiv:1509.04266 [cond-mat.str-el]

2016 arXiv
[37]

«Extended actions, dynamics of edge modes, and entanglement entropy».JHEP 09 (2020), p

Marc Geiller and Puttarak Jai-akson. «Extended actions, dynamics of edge modes, and entanglement entropy».JHEP 09 (2020), p. 134.doi: 10 . 1007 / JHEP09(2020)134. arXiv:1912.06025 [hep-th]

2020 arXiv
[38]

«Bosonic topo- logical phases of matter: Bulk-boundary correspondence, symmetry protected topological invariants, and gauging».Phys

Apoorv Tiwari, Xiao Chen, Ken Shiozaki, and Shinsei Ryu. «Bosonic topo- logical phases of matter: Bulk-boundary correspondence, symmetry protected topological invariants, and gauging».Phys. Rev. B97.24 (2018), p. 245133.doi: 10.1103/PhysRevB.97.245133. arXiv:1710.04730 [cond-m...

2018 arXiv
[39]

Adv.Theor.Math.Phys

EdwardWitten.«Anti-deSitterspaceandholography». Adv.Theor.Math.Phys. 2 (1998), pp. 253–291.doi: 10 . 4310 / ATMP . 1998 . v2 . n2 . a2. arXiv: hep - th / 9802150

1998
[40]

Klebanov

Igor R. Klebanov. «TASI lectures: Introduction to the AdS / CFT correspon- dence». Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 99): Strings, Branes, and Gravity. Sept. 2000, pp. 615–650. doi: 10 . 1142 / 9789812799630_0007. arXiv:hep-th/0009139

2000 arXiv
[41]

«Introduction to Gauge/Gravity Duality»

Joseph Polchinski. «Introduction to Gauge/Gravity Duality». Theoretical Ad- vanced Study Institute in Elementary Particle Physics: String theory and its Ap- plications: From meV to the Planck Scale. Oct. 2010, pp. 3–46. doi: 10 . 1142 / 9789814350525_0001. arXiv:1010.6134 [hep...

2010 arXiv
[42]

Hartnoll

Sean A. Hartnoll. «Lectures on holographic methods for condensed matter physics». Class. Quant. Grav.26 (2009). Ed. by A. M. Uranga, p. 224002.doi: 10.1088/0264-9381/26/22/224002. arXiv:0903.3246 [hep-th]

2009 arXiv
[43]

ChristopherP.Herzog.«LecturesonHolographicSuperfluidityandSupercon- ductivity». J. Phys. A42 (2009), p. 343001.doi: 10 . 1088 / 1751 - 8113 / 42 / 34 / 343001. arXiv:0904.1975 [hep-th]

2009 arXiv
[44]

HolographicDualityin CondensedMatterPhysics .CambridgeUniv.Press,2015

JanZaanen,Ya-WenSun,YanLiu,andKoenraadSchalm. HolographicDualityin CondensedMatterPhysics .CambridgeUniv.Press,2015. isbn:978-1-107-08008-9

2015
[45]

Lect.NotesPhys

SubirSachdev.«CondensedMatterandAdS/CFT». Lect.NotesPhys. 828(2011), pp. 273–311.doi: 10.1007/978-3-642-04864-7 _9. arXiv:1002.2947 [hep-th]

2011 arXiv
[46]

2013 Arnold Sommerfeld School on Gauge-gravity duality and condensed matter physics

J. McGreevy. Holography with and without gravity. Lectures held at the “2013 Arnold Sommerfeld School on Gauge-gravity duality and condensed matter physics”. url: https://www.theorie.physik.uni-muenchen.de/activities/ schools/archiv/2013_asc_school/videos_ads_cmt/mcgreevy/index.htmll

2013
[47]

«Holography in flat spacetime: 4D theories and electro- magnetic duality on the border»

AndreaAmoretti,AlessandroBraggio,GiacomoCaruso,NicolaMaggiore,and Nicodemo Magnoli. «Holography in flat spacetime: 4D theories and electro- magnetic duality on the border». JHEP 04 (2014), p. 142. doi: 10 . 1007 / JHEP04(2014)142. arXiv:1401.7101 [hep-th]

2014 arXiv
[48]

Jin, and G

E.Bocquillon,V.Freulon,J-.MBerroir,P.Degiovanni,B.Plaçais,A.Cavanna,Y. Jin, and G. Fève. «Separation of neutral and charge modes in one-dimensional chiral edge channels». Nature Communications 4.1 (2013). doi: 10 . 1038 / ncomms2788. url: https://doi.org/10.1038%2Fncomms2788

2013
[49]

«Conserved chiral currents on the boundary of 3D Maxwell theory»

Nicola Maggiore. «Conserved chiral currents on the boundary of 3D Maxwell theory». J. Phys. A52.11 (2019), p. 115401.doi: 10 . 1088 / 1751 - 8121 / ab045a. arXiv: 1902.01901 [hep-th]

2019 arXiv
[50]

Phys.Rev.Lett

ClaudioChamon.«QuantumGlassiness». Phys.Rev.Lett. 94.4(2005),p.040402. doi: 10.1103/physrevlett.94.040402. arXiv:cond-mat/0404182

2005 arXiv
[51]

JeongwanHaah.«Localstabilizercodesinthreedimensionswithoutstringlog- ical operators».Phys. Rev. A83.4 (2011), p. 042330.doi: 10.1103/physreva.83. 042330. arXiv:1101.1962 [quant-ph]

2011 arXiv
[52]

SagarVijay,JeongwanHaah,andLiangFu.«FractonTopologicalOrder,Gener- alized Lattice Gauge Theory and Duality».Phys. Rev. B94.23 (2016), p. 235157. doi: 10.1103/PhysRevB.94.235157. arXiv:1603.04442 [cond-mat.str-el]

2016 arXiv
[53]

SagarVijay,JeongwanHaah,andLiangFu.«ANewKindofTopologicalQuan- tum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations». Phys. Rev. B92.23 (2015), p. 235136.doi: 10.1103/PhysRevB.92. 235136. arXiv:1505.02576 [cond-mat.str-el]

2015 arXiv
[54]

Nandkishore and Michael Hermele

Rahul M. Nandkishore and Michael Hermele. «Fractons».Ann. Rev. Condensed Matter Phys. 10 (2019), pp. 295–313. doi: 10 . 1146 / annurev - conmatphys - 031218-013604. arXiv:1803.11196 [cond-mat.str-el]

2019 arXiv
[55]

«Fracton Phases of Matter».Int

Michael Pretko, Xie Chen, and Yizhi You. «Fracton Phases of Matter».Int. J. Mod.Phys.A 35.06(2020),p.2030003. doi: 10.1142/S0217751X20300033.arXiv: 2001.01722 [cond-mat.str-el]. bibliography 175

2020 arXiv
[56]

«ExoticU (1) Symmetries, Duality, and Fractonsin3+1-DimensionalQuantumFieldTheory»

Nathan Seiberg and Shu-Heng Shao. «ExoticU (1) Symmetries, Duality, and Fractonsin3+1-DimensionalQuantumFieldTheory». SciPostPhys. 9.4(2020), p. 046. doi: 10 . 21468 / SciPostPhys . 9 . 4 . 046 . arXiv: 2004 . 00015 [cond-mat.str-el]

2020
[57]

H. B. G. Casimir and D. Polder. «The Influence of retardation on the London- vanderWaalsforces». Phys.Rev. 73(1948),pp.360–372. doi: 10.1103/PhysRev. 73.360

1948 doi
[58]

H. Saleur. «Lectures on nonperturbative field theory and quantum impurity problems» (Dec. 1998). arXiv:cond-mat/9812110

1998 arXiv
[59]

H. Saleur. «Lectures on nonperturbative field theory and quantum impurity problems: Part 2» (July 2000). arXiv:cond-mat/0007309

2000 arXiv
[60]

Eduardo Fradkin and Joel E. Moore. «Entanglement entropy of 2D conformal quantumcriticalpoints:hearingtheshapeofaquantumdrum». Phys.Rev.Lett. 97 (2006), p. 050404.doi: 10.1103/PhysRevLett.97.050404. arXiv:cond-mat/ 0605683

2006 doi
[61]

Mintchev and E

M. Mintchev and E. Ragoucy. «Algebraic approach to multiple defects on the line and application to Casimir force».J. Phys. A40 (2007), p. 9515.doi: 10 . 1088/1751-8113/40/31/025. arXiv:0705.1322 [hep-th]

2007 arXiv
[62]

«The Large N limit of superconformal field theories andsupergravity»

Juan Martin Maldacena. «The Large N limit of superconformal field theories andsupergravity». Adv.Theor. Math.Phys. 2(1998), pp.231–252. doi: 10.4310/ ATMP.1998.v2.n2.a1. arXiv:hep-th/9711200

1998 arXiv
[63]

«Thermo-electric transport in gauge/gravity models».Adv

Andrea Amoretti, Alessandro Braggio, Nicola Maggiore, and Nicodemo Mag- noli. «Thermo-electric transport in gauge/gravity models».Adv. Phys. X2.2 (2017), pp. 409–427.doi: 10.1080/23746149.2017.1300509

2017
[64]

S. S. Gubser, Igor R. Klebanov, and Alexander M. Polyakov. «Gauge theory correlators from noncritical string theory».Phys. Lett. B428 (1998), pp. 105–

1998
[65]

«ChargedAdSblackholesandcatastrophicholography»

AndrewChamblin,RobertoEmparan,CliffordV.Johnson,andRobertC.Myers. «ChargedAdSblackholesandcatastrophicholography». Phys.Rev.D 60(1999), p. 064018.doi: 10.1103/PhysRevD.60.064018. arXiv:hep-th/9902170

1999 arXiv
[66]

S. W. Hawking and Don N. Page. «Thermodynamics of Black Holes in anti-De SitterSpace». Commun.Math.Phys. 87(1983),p.577. doi: 10.1007/BF01208266

1983 doi
[67]

Quantum Phase Transitions

Subir Sachdev. Quantum Phase Transitions. Cambridge University Press, Apr
[68]

Wess and J

J. Wess and J. Bagger. Supersymmetry and supergravity. Princeton, NJ, USA: Princeton University Press, 1992.isbn: 978-0-691-02530-8

1992
[69]

«Renormaliza- tion of Topological Field Theory».Nucl

Danny Birmingham, Mark Rakowski, and George Thompson. «Renormaliza- tion of Topological Field Theory».Nucl. Phys. B329 (1990), pp. 83–97.doi: 10. 1016/0550-3213(90)90058-L

1990
[70]

Jackiw, and S

Stanley Deser, R. Jackiw, and S. Templeton. «Topologically Massive Gauge Theories». Annals Phys.140 (1982). [Erratum: Annals Phys. 185, 406 (1988)], pp. 372–411.doi: 10.1016/0003-4916(82)90164-6. 176 bibliography

1982 doi
[71]

L. D. Faddeev and V. N. Popov. «Feynman Diagrams for the Yang-Mills Field». Phys. Lett. B25 (1967). Ed. by Jong-Ping Hsu and D. Fine, pp. 29–30.doi: 10 . 1016/0370-2693(67)90067-6

1967
[72]

Yang-Millstheoriesinalgebraicnoncovari- ant gauges: Canonical quantization and renormalization

A.Bassetto,G.Nardelli,andR.Soldati. Yang-Millstheoriesinalgebraicnoncovari- ant gauges: Canonical quantization and renormalization. 1991

1991
[73]

G. Mack. «Introduction to conformal invariant Quantum Field Theory in two- dimensions and more dimensions».NATO Advanced Summer Institute on Non- perturbative Quantum Field Theory (Cargese Summer Institute). Aug. 1988

1988
[75]

Peter Goddard and David I. Olive. «Kac-Moody and Virasoro Algebras in Re- lation to Quantum Physics».Int. J. Mod. Phys. A1 (1986), p. 303.doi: 10.1142/ S0217751X86000149

1986
[76]

Nucl.Phys.BProc.Suppl

A.BlasiandR.Collina.«Chern-SimonsmodelintheLandaugaugeanditscon- nectiontotheKac-Moodyalgebra». Nucl.Phys.BProc.Suppl. 18(1991),pp.16–

1991
[77]

Blasi, A

A. Blasi, A. Braggio, M. Carrega, D. Ferraro, N. Maggiore, and N. Magnoli. «Non-AbelianBFtheoryfor2+1dimensionaltopologicalstatesofmatter». New J. Phys.14 (2012), p. 013060.doi: 10 . 1088 / 1367 - 2630 / 14 / 1 / 013060. arXiv: 1106.4641 [cond-mat.mes-hall]

2012 arXiv
[78]

Schwinger

Julian S. Schwinger. «Field theory commutators».Phys. Rev. Lett.3 (1959). Ed. by K. A. Milton, pp. 296–297.doi: 10.1103/PhysRevLett.3.296

1959 doi
[79]

«Topological Quantum Field Theory».Commun

Edward Witten. «Topological Quantum Field Theory».Commun. Math. Phys. 117 (1988), p. 353.doi: 10.1007/BF01223371

1988 doi
[80]

doi: 10.1016/0920-5632(91)90118-X

doi
[81]

Becchi, A

C. Becchi, A. Rouet, and R. Stora. «Renormalization of the Abelian Higgs- Kibble Model».Commun. Math. Phys.42 (1975), pp. 127–162.doi: 10 . 1007 / BF01614158

1975
[82]

Annals Phys.98 (1976), pp

C.Becchi,A.Rouet,andR.Stora.«RenormalizationofGaugeTheories». Annals Phys.98 (1976), pp. 287–321.doi: 10.1016/0003-4916(76)90156-1

1976 doi
[83]

EdwardWitten.«OntheStructureoftheTopologicalPhaseofTwo-dimensional Gravity».Nucl. Phys. B340 (1990), pp. 281–332.doi: 10.1016/0550- 3213(90) 90449-N

1990 doi
[84]

«Quantum Field Theory and the Jones Polynomial».Commun

Edward Witten. «Quantum Field Theory and the Jones Polynomial».Commun. Math. Phys.121 (1989). Ed. by Asoke N. Mitra, pp. 351–399.doi: 10 . 1007 / BF01217730

1989
[85]

Commun.Math.Phys

EdwardWitten.«TopologicalSigmaModels». Commun.Math.Phys. 118(1988), p. 411.doi: 10.1007/BF01466725

1988 doi
[86]

AlbertS.Schwarz.«ThePartitionFunctionofDegenerateQuadraticFunctional and Ray-Singer Invariants».Lett. Math. Phys.2 (1978), pp. 247–252.doi: 10 . 1007/BF00406412. bibliography 177

1978
[87]

«From Chern–Simons to Tomonaga–Luttinger».Int

Nicola Maggiore. «From Chern–Simons to Tomonaga–Luttinger».Int. J. Mod. Phys.A 33.02(2018),p.1850013. doi: 10.1142/S0217751X18500136.arXiv: 1712. 08744 [hep-th]

2018 doi
[88]

«Introduction to cohomological field theories»

Edward Witten. «Introduction to cohomological field theories». Int. J. Mod. Phys. A6 (1991), pp. 2775–2792.doi: 10.1142/S0217751X91001350

1991 doi
[89]

X. G. Wen. «Chiral Luttinger Liquid and the Edge Excitations in the Fractional Quantum Hall States».Phys. Rev. B41 (1990), pp. 12838–12844.doi: 10.1103/ PhysRevB.41.12838

1990
[90]

Gerald V. Dunne. «Aspects of Chern-Simons theory». Les Houches Summer SchoolinTheoreticalPhysics,Session69:TopologicalAspectsofLow-dimensionalSys- tems. July 1998. arXiv:hep-th/9902115

1998 arXiv
[91]

«Lectures on the Quantum Hall Effect»

David Tong. «Lectures on the Quantum Hall Effect». June 2016. arXiv:1606 . 06687 [hep-th]

2016
[92]

AndreaAmoretti,AlessandroBraggio,GiacomoCaruso,NicolaMaggiore,and NicodemoMagnoli.«Introductionofaboundaryintopologicalfieldtheories». Phys. Rev. D90.12 (2014), p. 125006.doi: 10.1103/PhysRevD.90.125006. arXiv: 1410.2728 [hep-th]

2014 arXiv
[93]

H. Aratyn. «A Bose representation for the massless Dirac field in four- dimensions». Nucl. Phys. B 227 (1983), pp. 172–188. doi: 10 . 1016 / 0550 - 3213(83)90148-7

1983
[94]

Charles L. Kane. «Lectures on Bosonization». url: https : / / api . semanticscholar.org/CorpusID:41254493
[95]

LiangFu,C.Kane,andE.Mele.«TopologicalInsulatorsinThreeDimensions». Phys. Rev. Lett.98.10 (2007), p. 106803.doi: 10.1103/PhysRevLett.98.106803. arXiv: cond-mat/0607699

2007 arXiv
[96]

H. Aratyn. «fermions from bosons in (2+1)-dimensions». Phys. Rev. D 28 (1983), pp. 2016–2018.doi: 10.1103/PhysRevD.28.2016

1983 doi
[97]

X. G. Wen. «Electrodynamical Properties of Gapless Edge Excitations in the Fractional Quantum Hall States».Phys. Rev. Lett.64 (1990), p. 2206.doi: 10 . 1103/PhysRevLett.64.2206

1990
[98]

C. L. Kane and Matthew P. A. Fisher. «Impurity scattering and transport of fractionalquantumHalledgestates». PhysicalReviewB 51.19(1995),pp.13449– 13466. doi: 10 . 1103 / physrevb . 51 . 13449. url: https : / / doi . org / 10 . 1103 % 2Fphysrevb.51.13449

1995
[99]

32–43.issn: 2405-4283.doi: https://doi.org/10.1016/ j

MasayukiHashisakaandToshimasaFujisawa.«Tomonaga–Luttinger-liquidna- ture of edge excitations in integer quantum Hall edge channels».Reviews in Physics 3 (2018), pp. 32–43.issn: 2405-4283.doi: https://doi.org/10.1016/ j . revip . 2018 . 07 . 001. url: https : / / www . scienced...

2018
[100]

X. G. Wen. «Gapless Boundary Excitations in the Quantum Hall States and in the Chiral Spin States».Phys. Rev. B43 (1991), pp. 11025–11036.doi: 10.1103/ PhysRevB.43.11025

1991
[101]

R.FloreaniniandR.Jackiw.«SelfdualFieldsasChargeDensitySolitons». Phys. Rev. Lett.59 (1987), p. 1873.doi: 10.1103/PhysRevLett.59.1873

1987 doi
[102]

B. E. Kane, D. C. Tsui, and G. Weimann. «Evidence for edge currents in the integral quantum Hall effect».Phys. Rev. Lett.59 (12 1987), pp. 1353–1356.doi: 10.1103/PhysRevLett.59.1353 . url: https://link.aps.org/doi/10.1103/ PhysRevLett.59.1353

1987 doi
[103]

Wald.General Relativity

Robert M. Wald.General Relativity. Chicago, USA: Chicago Univ. Pr., 1984.doi: 10.7208/chicago/9780226870373.001.0001

1984
[104]

doi: 10.1016/0370-2693(90)90963-7

doi
[105]

«Edge transport properties of the fractional quantum Hall states and weak-impurity scattering of a one-dimensional charge-density wave».Phys

Xiao-Gang Wen. «Edge transport properties of the fractional quantum Hall states and weak-impurity scattering of a one-dimensional charge-density wave».Phys. Rev. B44.11 (1991), p. 5708.doi: 10.1103/PhysRevB.44.5708. 178 bibliography

1991 doi
[106]

d’Inverno

R. d’Inverno. Introducing Einstein’s relativity. 1992.isbn: 978-0-19-859686-8

1992
[107]

«Covariant Quantization of the Electromagnetic Field in the Landau Gauge».Prog

Noboru Nakanishi. «Covariant Quantization of the Electromagnetic Field in the Landau Gauge».Prog. Theor. Phys.35 (1966), pp. 1111–1116.doi: 10.1143/ PTP.35.1111

1966
[108]

Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity

Steven Weinberg. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: John Wiley and Sons, 1972.isbn: 978- 0-471-92567-5, 978-0-471-92567-5

1972
[109]

Sean M. Carroll. Spacetime and Geometry: An Introduction to General Relativ- ity. Cambridge University Press, July 2019.isbn: 978-0-8053-8732-2, 978-1-108- 48839-6, 978-1-108-77555-7

2019
[110]

Nucl.Phys.B 924(2017),pp.312–365

MarcGeiller.«Edgemodesandcornerambiguitiesin3dChern–Simonstheory andgravity». Nucl.Phys.B 924(2017),pp.312–365. doi: 10.1016/j.nuclphysb. 2017.09.010. arXiv:1703.04748 [gr-qc]

2017 arXiv
[111]

Nash and S

C. Nash and S. Sen.Topology and geometry for physicists. 1983

1983
[112]

B.Lautrup.«Canonicalquantumelectrodynamicsincovariantgauges»(1967)

1967
[113]

Moore, Adam Schwimmer, and Nathan Seiberg

Shmuel Elitzur, Gregory W. Moore, Adam Schwimmer, and Nathan Seiberg. «RemarksontheCanonicalQuantizationoftheChern-Simons-WittenTheory». Nucl. Phys. B326 (1989), pp. 108–134.doi: 10.1016/0550-3213(89)90436-7

1989 doi
[114]

arXiv:hep-th/9802109

doi: 10.1016/S0370-2693(98)00377-3. arXiv:hep-th/9802109

arXiv
[115]

I.PropertiesoftheLuttingermodelandtheirextensiontothegeneral1Dinter- acting spinless Fermi gas».J

F.D.M.Haldane.«Luttingerliquidtheoryofone-dimensionalquantumfluids. I.PropertiesoftheLuttingermodelandtheirextensiontothegeneral1Dinter- acting spinless Fermi gas».J. Phys. C14 (1981), pp. 2585–2609.doi: 10.1088/ 0022-3719/14/19/010

1981
[116]

FoundationsofDifferentiableManifoldsandLieGroups .SpringerVer- lag, 1983

W.WarnerF. FoundationsofDifferentiableManifoldsandLieGroups .SpringerVer- lag, 1983

1983
[117]

M. Basler. «Functional methods for arbitrary densities in curved space-time». Fortsch. Phys.41 (1993), pp. 1–43

1993
[118]

Frohlich and T

J. Frohlich and T. Kerler. «Universality in quantum Hall systems».Nucl. Phys. B 354 (1991), pp. 369–417.doi: 10.1016/0550-3213(91)90360-A

1991 doi
[119]

Physical Review B96.8 (2017).doi: 10.1103/physrevb.96.081101

Paul Brasseur, Ngoc Han Tu, Yoshiaki Sekine, Koji Muraki, Masayuki Hashisaka,ToshimasaFujisawa,andNorioKumada.«Chargefractionalization in artificial Tomonaga-Luttinger liquids with controlled interaction strength». Physical Review B96.8 (2017).doi: 10.1103/physrevb.96.081101 ....

2017 doi
[120]

Ann.Phys

I.Safi.«Propriétésd’unfilquantiqueconnectéàdesfilsdemesure». Ann.Phys. Fr.22.5 (1997).doi: 10.1051/anphys:199705001

1997 doi
[121]

Perfetto, G

E. Perfetto, G. Stefanucci, H. Kamata, and T. Fujisawa. «Time-resolved charge fractionalization in inhomogeneous Luttinger liquids».Physical Review B89.20 (2014). doi: 10.1103/physrevb.89.201413 . url: https://doi.org/10.1103% 2Fphysrevb.89.201413. bibliography 179

2014 doi
[122]

177–181.doi: 10.1038/nnano.2013.312

H.Kamata,N.Kumada,M.Hashisaka,K.Muraki,andT.Fujisawa.«Fractional- ized wave packets from an artificial Tomonaga–Luttinger liquid».Nature Nan- otechnology9.3 (2014), pp. 177–181.doi: 10.1038/nnano.2013.312. url: https: //doi.org/10.1038%2Fnnano.2013.312

2014 doi
[123]

T. Can, M. Laskin, and P. Wiegmann. «Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response».Phys. Rev. Lett.113 (2014), p. 046803.doi: 10.1103/PhysRevLett.113.046803. arXiv: 1402.1531 [cond-mat.str-el]

2014 arXiv
[124]

Chaojing Lin, Masayuki Hashisaka, Takafumi Akiho, Koji Muraki, and Toshi- masa Fujisawa. «Time-resolved investigation of plasmon mode along interface channels in integer and fractional quantum Hall regimes».Physical Review B 104.12 (2021).doi: 10.1103/physrevb.104.125304. url:...

2021 doi
[125]

«Unconventional frac- tional quantum Hall states and Wigner crystallization in suspended Corbino graphene»

Manohar Kumar, Antti Laitinen, and Pertti Hakonen. «Unconventional frac- tional quantum Hall states and Wigner crystallization in suspended Corbino graphene». Nature Communications 9.1 (2018). doi: 10 . 1038 / s41467 - 018 - 05094-8. url: https://doi.org/10.1038%2Fs41467-018-05094-8

2018
[126]

Glenn Wagner, Fernando de Juan, and Dung X. Nguyen. «Landau levels in curved space realized in strained graphene».SciPost Phys. Core5 (2022), p. 029. doi: 10 . 21468 / SciPostPhysCore . 5 . 2 . 029 . arXiv: 1911 . 02028 [cond-mat.str-el]

2022
[127]

«Quantized Anomalous Hall Effect in Magnetic Topological Insulators»

Rui Yu, Wei Zhang, Hai-Jun Zhang, Shou-Cheng Zhang, Xi Dai, and Zhong Fang. «Quantized Anomalous Hall Effect in Magnetic Topological Insulators». Science329.5987(2010),pp.61–64. doi: 10.1126/science.1187485.arXiv: 1002. 0946 [cond-mat.mes-hall]

2010 doi
[128]

Xiao-GangWen.«TopologicalordersandedgeexcitationsinFQHstates». Adv. Phys. 44.5 (1995), pp. 405–473.doi: 10.1080/00018739500101566. arXiv:cond- mat/9506066

1995
[129]

Andrei Bernevig, and Shou-Cheng Zhang

Congjun Wu, B. Andrei Bernevig, and Shou-Cheng Zhang. «Helical Liquid and the Edge of Quantum Spin Hall Systems».Phys. Rev. Lett.96 (10 2006), p.106401. doi: 10.1103/PhysRevLett.96.106401. url: https://link.aps.org/ doi/10.1103/PhysRevLett.96.106401

2006 doi
[130]

«Quantum Anomalous Hall Effect in Hg(1-y)Mn(y)Te Quantum Wells».Phys

Chao-Xing Liu, Xiao-Liang Qi, Xi Dai, Zhong Fang, and Shou-Cheng Zhang. «Quantum Anomalous Hall Effect in Hg(1-y)Mn(y)Te Quantum Wells».Phys. Rev. Lett.101 (2008), p. 146802.doi: 10.1103/PhysRevLett.101.146802. arXiv: 0802.2711 [cond-mat.mes-hall]

2008 arXiv
[131]

Středa and P

P. Středa and P. Šeba. «Antisymmetric Spin Filtering in One-Dimensional Elec- tronSystemswithUniformSpin-OrbitCoupling». Phys.Rev.Lett. 90(252003), p.256601. doi: 10.1103/PhysRevLett.90.256601. url: https://link.aps.org/ doi/10.1103/PhysRevLett.90.256601

doi
[132]

X. G. Wen.Quantum field theory of many-body systems: From the origin of sound to an origin of light and electrons. 2004. 180 bibliography

2004
[133]

«Time-resolved pure spin fractionalization and spin-charge separation in he- lical Luttinger liquid based devices».Physical Review B92.19 (2015)

Alessio Calzona, Matteo Carrega, Giacomo Dolcetto, and Maura Sassetti. «Time-resolved pure spin fractionalization and spin-charge separation in he- lical Luttinger liquid based devices».Physical Review B92.19 (2015). doi: 10 . 1103/physrevb.92.195414 . url: https://doi.org/10....

2015
[134]

«Strongly anisotropic spin response as a signa- ture of the helical regime in Rashba nanowires».Physical Review B88.3 (2013)

Tobias Meng and Daniel Loss. «Strongly anisotropic spin response as a signa- ture of the helical regime in Rashba nanowires».Physical Review B88.3 (2013). doi: 10 . 1103 / physrevb . 88 . 035437 . url: https : / / doi . org / 10 . 1103 % 2Fphysrevb.88.035437

2013
[135]

M. O. Goerbig, J.-N. Fuchs, G. Montambaux, and F. Piéchon.Physical Review B 78.4 (2008). doi: 10 . 1103 / physrevb . 78 . 045415. url: https : / / doi . org / 10 . 1103%2Fphysrevb.78.045415

2008
[136]

Heedt, N

S. Heedt, N. Traverso Ziani, F. Crépin, W. Prost, St. Trellenkamp, J. Schubert, D. Grützmacher, B. Trauzettel, and Th. Schäpers. «Signatures of interaction- inducedhelicalgapsinnanowirequantumpointcontacts». NaturePhysics 13.6 (2017),pp.563–567. doi: 10.1038/nphys4070. url: ht...

2017 doi
[137]

Soluyanov, Dominik Gresch, Zhijun Wang, QuanSheng Wu, Matthias Troyer, Xi Dai, and B

Alexey A. Soluyanov, Dominik Gresch, Zhijun Wang, QuanSheng Wu, Matthias Troyer, Xi Dai, and B. Andrei Bernevig. «Type-II Weyl semimetals». Nature 527.7579 (2015), pp. 495–498.doi: 10 . 1038 / nature15768. url: https : //doi.org/10.1038%2Fnature15768

2015
[138]

SergueiTchoumakov,MarcelloCivelli,andMarkO.Goerbig.«Magnetic-Field- Induced Relativistic Properties in Type-I and Type-II Weyl Semimetals».Phys. Rev. Lett.117 (8 2016), p. 086402.doi: 10.1103/PhysRevLett.117.086402. url: https://link.aps.org/doi/10.1103/PhysRevLett.117.086402

2016 doi
[139]

«Bulk-Boundary Correspondence in the Quantum Hall Effect».J

Andrea Cappelli and Lorenzo Maffi. «Bulk-Boundary Correspondence in the Quantum Hall Effect».J. Phys. A51.36 (2018), p. 365401.doi: 10.1088/1751- 8121/aad0ab. arXiv:1801.03759 [hep-th]. bibliography 181

2018 arXiv
[140]

Rodriguez, François D

Giacomo Rebora, Dario Ferraro, Ramiro H. Rodriguez, François D. Parmen- tier, Patrice Roche, and Maura Sassetti. «Electronic Wave-Packets in Integer Quantum Hall Edge Channels: Relaxation and Dissipative Effects».Entropy 23.2 (2021), p. 138.doi: 10.3390/e23020138. url: https:/...

2021 doi
[141]

John L. Cardy. «Boundary conformal field theory» (Nov. 2004). arXiv:hep - th/0411189

2004
[142]

A.BlasiandR.Collina.«TheChern-Simonsmodelwithboundary:ACohomo- logical approach».Int. J. Mod. Phys. A7 (1992), pp. 3083–3104.doi: 10.1142/ S0217751X92001381

1992
[143]

Blasi, N

A. Blasi, N. Maggiore, N. Magnoli, and S. Storace. «Maxwell-Chern-Simons TheoryWithBoundary». Class.Quant.Grav. 27(2010),p.165018. doi: 10.1088/ 0264-9381/27/16/165018. arXiv:1002.3227 [hep-th]

2010 arXiv
[144]

«Three-dimensional TopologicalInsulatorsandBosonization»

Andrea Cappelli, Enrico Randellini, and Jacopo Sisti. «Three-dimensional TopologicalInsulatorsandBosonization». JHEP05(2017),p.135. doi: 10.1007/ JHEP05(2017)135. arXiv:1612.05212 [cond-mat.str-el]

2017 arXiv
[145]

«Clas- sificationoftopologicalinsulatorsandsuperconductorsinthreespatialdimen- sions».Phys.Rev

Andreas Schnyder, Shinsei Ryu, Akira Furusaki, and Andreas Ludwig. «Clas- sificationoftopologicalinsulatorsandsuperconductorsinthreespatialdimen- sions».Phys.Rev. B78.19(2008),p. 195125. doi: 10.1103/PhysRevB.78.195125. arXiv: 0803.2786 [cond-mat.mes-hall]

2008 arXiv
[146]

«Three-dimensional dynamics of four-dimensional topological BF theory with boundary»

Andrea Amoretti, Alberto Blasi, Nicola Maggiore, and Nicodemo Magnoli. «Three-dimensional dynamics of four-dimensional topological BF theory with boundary». New J. Phys.14 (2012), p. 113014.doi: 10.1088/1367-2630/14/11/ 113014. arXiv:1205.6156 [hep-th]

2012 arXiv
[147]

Dimitra Karabali and V. P. Nair. «Boundary Conditions as Dynamical Fields». Phys. Rev. D92.12 (2015), p. 125003.doi: 10.1103/PhysRevD.92.125003. arXiv: 1507.03880 [hep-th]

2015 arXiv
[148]

«Holographic reduction of Maxwell-Chern-Simons theory»

Nicola Maggiore. «Holographic reduction of Maxwell-Chern-Simons theory». Eur.Phys.J.Plus 133.7(2018),p.281. doi: 10.1140/epjp/i2018-12130-y.arXiv: 1807.09960 [hep-th]

2018 arXiv
[149]

«Topologically protected duality on the boundary of Maxwell-BF theory».Symmetry 11 (2019), p

Alberto Blasi and Nicola Maggiore. «Topologically protected duality on the boundary of Maxwell-BF theory».Symmetry 11 (2019), p. 921.doi: 10 . 3390 / sym11070921. arXiv:1907.08764 [hep-th]

2019 arXiv
[150]

«Black hole as topological insulator (II): the boundary modes» (June 2017)

Jingbo Wang. «Black hole as topological insulator (II): the boundary modes» (June 2017). arXiv:1706.01630 [gr-qc]

2017 arXiv
[151]

«Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting».SciPost Phys.9 (2020), p

Dung Xuan Nguyen, Andrey Gromov, and Sergej Moroz. «Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting».SciPost Phys.9 (2020), p. 076.doi: 10.21468/SciPostPhys. 9.5.076. arXiv:2005.12317 [cond-mat.quant-gas]

2020 arXiv
[152]

«Fracton-Elasticity Duality».Phys

Michael Pretko and Leo Radzihovsky. «Fracton-Elasticity Duality».Phys. Rev. Lett. 120.19 (2018), p. 195301.doi: 10.1103/PhysRevLett.120.195301 . arXiv: 1711.11044 [cond-mat.str-el]

2018 arXiv
[153]

«On duality between Cosserat elasticity andfractons»

Andrey Gromov and Piotr Surówka. «On duality between Cosserat elasticity andfractons». SciPostPhys. 8.4(2020),p.065. doi: 10.21468/SciPostPhys.8.4

2020 doi
[154]

arXiv:1908.06984 [cond-mat.str-el]

1908 arXiv
[155]

«Emergent dipole gauge fields and fractons».Phys

Alessio Caddeo, Carlos Hoyos, and Daniele Musso. «Emergent dipole gauge fields and fractons».Phys. Rev. D106.11 (2022), p. L111903.doi: 10 . 1103 / PhysRevD.106.L111903. arXiv:2206.12877 [cond-mat.str-el]

2022 arXiv
[156]

«Hydro- dynamicsofdipole-conservingfluids»

Aleksander Głódkowski, Francisco Peña Benítez, and Piotr Surówka. «Hydro- dynamicsofdipole-conservingfluids». Phys.Rev.E 107.3(2023),p.034142. doi: 10.1103/PhysRevE.107.034142. arXiv:2212.06848 [cond-mat.str-el]

2023 arXiv
[157]

Nandkishore

Andrey Gromov, Andrew Lucas, and Rahul M. Nandkishore. «Fracton hy- drodynamics». Phys. Rev. Res. 2.3 (2020), p. 033124. doi: 10 . 1103 / PhysRevResearch.2.033124. arXiv:2003.09429 [cond-mat.str-el]

2020 arXiv
[158]

Chen, and Peng Ye

Jian-Keng Yuan, Shuai A. Chen, and Peng Ye. «Fractonic Superfluids».Phys. Rev.Res. 2.2(2020),p.023267. doi: 10.1103/PhysRevResearch.2.023267.arXiv: 1911.02876 [cond-mat.str-el]. 182 bibliography

2020 arXiv
[159]

«Non-Abelian gauged fracton matter field theory: Sigma models, superfluids, and vortices».Phys

Juven Wang and Shing-Tung Yau. «Non-Abelian gauged fracton matter field theory: Sigma models, superfluids, and vortices».Phys. Rev. Res.2.4 (2020), p. 043219. doi: 10 . 1103 / PhysRevResearch . 2 . 043219 . arXiv: 1912 . 13485 [cond-mat.str-el]

2020
[160]

Grosvenor, Carlos Hoyos, Francisco Peña Benítez, and Piotr Surówka

Kevin T. Grosvenor, Carlos Hoyos, Francisco Peña Benítez, and Piotr Surówka. «Hydrodynamics of ideal fracton fluids».Phys. Rev. Res.3.4 (2021), p. 043186. doi: 10 . 1103 / PhysRevResearch . 3 . 043186 . arXiv: 2105 . 01084 [cond-mat.str-el]

2021
[161]

MichaelPretko.«SubdimensionalParticleStructureofHigherRankU(1)Spin Liquids». Phys. Rev. B95.11 (2017), p. 115139.doi: 10 . 1103 / PhysRevB . 95 . 115139. arXiv:1604.05329 [cond-mat.str-el]

2017 arXiv
[162]

«Dynamical Scar States in Driven Fracton Sys- tems».Phys.Rev.Lett

Shriya Pai and Michael Pretko. «Dynamical Scar States in Driven Fracton Sys- tems».Phys.Rev.Lett. 123.13(2019),p.136401. doi: 10.1103/PhysRevLett.123. 136401. arXiv:1903.06173 [cond-mat.stat-mech]

2019 arXiv
[163]

«Localization fromHilbertspaceshattering:Fromtheorytophysicalrealizations»

Vedika Khemani, Michael Hermele, and Rahul Nandkishore. «Localization fromHilbertspaceshattering:Fromtheorytophysicalrealizations». Phys.Rev. B 101.17 (2020), p. 174204.doi: 10.1103/PhysRevB.101.174204 . arXiv: 1904. 04815 [cond-mat.stat-mech]

2020 doi
[164]

«Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians».Phys

Pablo Sala, Tibor Rakovszky, Ruben Verresen, Michael Knap, and Frank Pollmann. «Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians».Phys. Rev. X10.1 (2020), p. 011047.doi: 10. 1103/PhysRevX.10.011047. arXiv:1904.04266 [cond-mat.str-el]

2020 arXiv
[165]

«Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story»

Michael Pretko. «Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story». Phys. Rev. B 96.3 (2017), p. 035119. doi: 10 . 1103 / PhysRevB.96.035119. arXiv:1606.08857 [cond-mat.str-el]

2017 arXiv
[166]

Williamson, Zhen Bi, and Meng Cheng

Dominic J. Williamson, Zhen Bi, and Meng Cheng. «Fractonic Matter in Symmetry-EnrichedU(1)GaugeTheory». Phys.Rev.B 100.12(2019),p.125150. doi: 10.1103/PhysRevB.100.125150. arXiv:1809.10275 [cond-mat.str-el]. bibliography 183

2019 arXiv
[167]

«The Higgs Mechanism in Higher- Rank Symmetric U (1) Gauge Theories».Phys

Daniel Bulmash and Maissam Barkeshli. «The Higgs Mechanism in Higher- Rank Symmetric U (1) Gauge Theories».Phys. Rev. B97.23 (2018), p. 235112. doi: 10.1103/PhysRevB.97.235112. arXiv:1802.10099 [cond-mat.str-el]

2018 arXiv
[168]

WilburShirley,KevinSlagle,ZhenghanWang,andXieChen.«FractonModels on General Three-Dimensional Manifolds».Phys. Rev. X8.3 (2018), p. 031051. doi: 10.1103/PhysRevX.8.031051. arXiv:1712.05892 [cond-mat.str-el]

2018 arXiv
[169]

«Fracton topological order via coupled layers».Phys

Han Ma, Ethan Lake, Xie Chen, and Michael Hermele. «Fracton topological order via coupled layers».Phys. Rev. B95.24 (2017), p. 245126.doi: 10.1103/ PhysRevB.95.245126. arXiv:1701.00747 [cond-mat.str-el]

2017 arXiv
[170]

«Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory».Phys

Han Ma, Michael Hermele, and Xie Chen. «Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory».Phys. Rev. B98.3 (2018), p. 035111.doi: 10.1103/PhysRevB.98.035111 . arXiv:1802. 10108 [cond-mat.str-el]

2018 doi
[171]

«Fractons,dipolesymmetriesandcurvedspacetime»

Leo Bidussi, Jelle Hartong, Emil Have, Jørgen Musaeus, and Stefan Prohazka. «Fractons,dipolesymmetriesandcurvedspacetime». SciPostPhys. 12.6(2022), p. 205.doi: 10.21468/SciPostPhys.12.6.205. arXiv:2111.03668 [hep-th]

2022 arXiv
[172]

«Foliated Quantum Field Theory of Fracton Order».Phys

Kevin Slagle. «Foliated Quantum Field Theory of Fracton Order».Phys. Rev. Lett. 126.10 (2021), p. 101603.doi: 10.1103/PhysRevLett.126.101603 . arXiv: 2008.03852 [hep-th]

2021 arXiv
[173]

«Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry».Phys

Kevin Slagle and Yong Baek Kim. «Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry».Phys. Rev. B96.19 (2017), p. 195139. doi: 10 . 1103 / PhysRevB . 96 . 195139. arXiv: 1708 . 04619 [cond-mat.str-el]

2017
[174]

«Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order».SciPost Phys

Kevin Slagle, David Aasen, and Dominic Williamson. «Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order».SciPost Phys. 6.4 (2019), p. 043.doi: 10 . 21468 / SciPostPhys . 6 . 4 . 043. arXiv: 1812 . 01613 [cond-mat.str-el]

2019
[175]

«Symmetric Tensor Gauge Theories on Curved Spaces».Annals Phys.410 (2019), p

Kevin Slagle, Abhinav Prem, and Michael Pretko. «Symmetric Tensor Gauge Theories on Curved Spaces».Annals Phys.410 (2019), p. 167910.doi: 10.1016/ j.aop.2019.167910. arXiv:1807.00827 [cond-mat.str-el]

2019
[176]

Hartnoll, Pavel Kovtun, Hong Liu, Márk Mezei, Al- berto Nicolis, Riccardo Penco, Shu-Heng Shao, and Dam Thanh Son

Tomas Brauner, Sean A. Hartnoll, Pavel Kovtun, Hong Liu, Márk Mezei, Al- berto Nicolis, Riccardo Penco, Shu-Heng Shao, and Dam Thanh Son. «Snow- mass White Paper: Effective Field Theories for Condensed Matter Systems». Snowmass 2021. Mar. 2022. arXiv:2203.10110 [hep-th]

2021 arXiv
[177]

«Fractons in curved space».SciPost Phys.12.4 (2022), p

Akash Jain and Kristan Jensen. «Fractons in curved space».SciPost Phys.12.4 (2022), p. 142. doi: 10 . 21468 / SciPostPhys . 12 . 4 . 142. arXiv: 2111 . 03973 [hep-th]

2022
[178]

«Fracton-elasticity duality on curved manifolds» (Apr

LazarosTsaloukidis,JoséJ.Fernández-Melgarejo,JavierMolina-Vilaplana,and Piotr Surówka. «Fracton-elasticity duality on curved manifolds» (Apr. 2023). arXiv: 2304.12242 [hep-th]

2023 arXiv
[179]

«Hyperbolic fracton model, subsystem symmetry, and holography»

Han Yan. «Hyperbolic fracton model, subsystem symmetry, and holography». Phys. Rev. B99.15 (2019), p. 155126.doi: 10.1103/PhysRevB.99.155126. arXiv: 1807.05942 [hep-th]

2019 arXiv
[180]

«Higher-Spin Witten Effect and Two-Dimensional Fracton Phases»

Michael Pretko. «Higher-Spin Witten Effect and Two-Dimensional Fracton Phases». Phys. Rev. B96.12 (2017), p. 125151.doi: 10 . 1103 / PhysRevB . 96 . 125151. arXiv:1707.03838 [cond-mat.str-el]

2017 arXiv
[181]

Rosenberg and M

G. Rosenberg and M. Franz. «Witten effect in a crystalline topological insula- tor». Phys. Rev. B82 (2010), p. 035105.doi: 10 . 1103 / PhysRevB . 82 . 035105. arXiv: 1001.3179 [cond-mat.mes-hall]

2010 arXiv
[182]

«Emergent gravity of fractons: Mach’s principle revisited»

Michael Pretko. «Emergent gravity of fractons: Mach’s principle revisited». Phys. Rev. D96.2 (2017), p. 024051.doi: 10.1103/PhysRevD.96.024051 . arXiv: 1702.07613 [cond-mat.str-el]

2017 arXiv
[183]

«The theory of symmetric tensor field: From fractons to gravitons and back».Phys

Alberto Blasi and Nicola Maggiore. «The theory of symmetric tensor field: From fractons to gravitons and back».Phys. Lett. B833 (2022), p. 137304.doi: 10.1016/j.physletb.2022.137304. arXiv:2207.05956 [hep-th]

2022
[184]

D. Tong. Lectures on Gauge Theory. url: https://www.damtp.cam.ac.uk/user/ tong/gaugetheory.html
[185]

Phys.Lett.B 86(1979),pp.283–

EdwardWitten.«DyonsofChargeetheta/2pi». Phys.Lett.B 86(1979),pp.283–

1979
[186]

Stable Gapless Bose Liquid Phases without any Symmetry

Alex Rasmussen, Yi-Zhuang You, and Cenke Xu. Stable Gapless Bose Liquid Phases without any Symmetry. 2016. arXiv:1601.08235 [cond-mat.str-el]

2016 arXiv
[187]

«The Fracton Gauge Principle»

Michael Pretko. «The Fracton Gauge Principle». Phys. Rev. B 98.11 (2018), p. 115134. doi: 10 . 1103 / PhysRevB . 98 . 115134 . arXiv: 1807 . 11479 [cond-mat.str-el]

2018
[188]

Burnell, Trithep Devakul, Pranay Gorantla, Ho Tat Lam, and Shu- Heng Shao

Fiona J. Burnell, Trithep Devakul, Pranay Gorantla, Ho Tat Lam, and Shu- Heng Shao. «Anomaly inflow for subsystem symmetries».Phys. Rev. B106.8 (2022), p. 085113.doi: 10 . 1103 / PhysRevB . 106 . 085113. arXiv: 2110 . 09529 [cond-mat.str-el]

2022
[189]

Yizhi You, Trithep Devakul, S. L. Sondhi, and F. J. Burnell. «Fractonic Chern- Simons and BF theories».Phys. Rev. Res.2.2 (2020), p. 023249.doi: 10 . 1103 / PhysRevResearch.2.023249. arXiv:1904.11530 [cond-mat.str-el]

2020 arXiv
[190]

Yizhi You, F. J. Burnell, and Taylor L. Hughes. «Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons».Phys. Rev. B103.24 (2021), p. 245128.doi: 10 . 1103 / PhysRevB . 103 . 245128. arXiv: 1909.05868 [cond-mat.str-el]

2021 arXiv
[191]

105.doi: 10

AndreaCappelliandEnricoRandellini.«MultipoleExpansionintheQuantum Hall Effect».JHEP 03 (2016), p. 105.doi: 10 . 1007 / JHEP03(2016 ) 105. arXiv: 1512.02147 [cond-mat.str-el]

2016 arXiv
[192]

«Deciphering the nonlocal entanglement en- tropy of fracton topological orders».Phys

Bowen Shi and Yuan-Ming Lu. «Deciphering the nonlocal entanglement en- tropy of fracton topological orders».Phys. Rev. B97.14 (2018), p. 144106.doi: 10.1103/PhysRevB.97.144106. arXiv:1705.09300 [cond-mat.str-el]

2018 arXiv
[193]

RiccardoArgurio,CarlosHoyos,DanieleMusso,andDanielNaegels.«Fractons in effective field theories for spontaneously broken translations».Phys. Rev. D 104.10 (2021), p. 105001.doi: 10 . 1103 / PhysRevD . 104 . 105001. arXiv: 2107 . 03073 [hep-th]. bibliography 185

2021
[194]

«Exotic topological order in fractal spin liquids».Phys

Beni Yoshida. «Exotic topological order in fractal spin liquids».Phys. Rev. B 88.12 (2013), p. 125122.doi: 10.1103/PhysRevB.88.125122 . arXiv:1302.6248 [cond-mat.str-el]

2013 arXiv
[195]

«Emergent Phases of Fractonic Matter».Phys

Abhinav Prem, Michael Pretko, and Rahul Nandkishore. «Emergent Phases of Fractonic Matter».Phys. Rev. B97.8 (2018), p. 085116.doi: 10.1103/PhysRevB. 97.085116. arXiv:1709.09673 [cond-mat.str-el]

2018 arXiv
[196]

«Glassy quantum dynamics in translation invariant fracton models».Phys

Abhinav Prem, Jeongwan Haah, and Rahul Nandkishore. «Glassy quantum dynamics in translation invariant fracton models».Phys. Rev. B95.15 (2017), p. 155133. doi: 10 . 1103 / PhysRevB . 95 . 155133 . arXiv: 1702 . 02952 [cond-mat.stat-mech]

2017
[197]

«Quantum Self-Correction in the 3D Cu- bic Code Model»

Sergey Bravyi and Jeongwan Haah. «Quantum Self-Correction in the 3D Cu- bic Code Model». Phys. Rev. Lett.111 (20 2013), p. 200501. doi: 10 . 1103 / PhysRevLett . 111 . 200501. url: https : / / link . aps . org / doi / 10 . 1103 / PhysRevLett.111.200501

2013
[198]

«Gapless bosonic excitation without symmetry breaking: An alge- braic spin liquid with soft gravitons».Phys

Cenke Xu. «Gapless bosonic excitation without symmetry breaking: An alge- braic spin liquid with soft gravitons».Phys. Rev. B74 (22 2006), p. 224433.doi: 10.1103/PhysRevB.74.224433 . url: https://link.aps.org/doi/10.1103/ PhysRevB.74.224433

2006 doi
[199]

«Emergence of helicity +- 2 modes (gravitons) from qbit models».Nucl

Zheng-Cheng Gu and Xiao-Gang Wen. «Emergence of helicity +- 2 modes (gravitons) from qbit models».Nucl. Phys. B863 (2012), pp. 90–129.doi: 10 . 1016/j.nuclphysb.2012.05.010. arXiv:0907.1203 [gr-qc]

2012 arXiv
[200]

«Finite-temperature screening ofU(1) fractons».Phys

Michael Pretko. «Finite-temperature screening ofU(1) fractons».Phys. Rev. B 96(112017),p.115102. doi: 10.1103/PhysRevB.96.115102. url: https://link. aps.org/doi/10.1103/PhysRevB.96.115102

doi
[201]

«Towards classification of Fracton phases: the multipole al- gebra»

Andrey Gromov. «Towards classification of Fracton phases: the multipole al- gebra». Phys. Rev. X9.3 (2019), p. 031035.doi: 10.1103/PhysRevX.9.031035 . arXiv: 1812.05104 [cond-mat.str-el]

2019 arXiv
[202]

«Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons»

Pranay Gorantla, Ho Tat Lam, Nathan Seiberg, and Shu-Heng Shao. «Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons». Phys.Rev.B 106.4(2022),p.045112. doi: 10.1103/PhysRevB.106.045112.arXiv: 2201.10589 [cond-mat.str-el]

2022 arXiv
[203]

«Crystal-to-Fracton Tensor Gauge Theory Dualities».Phys

Michael Pretko, Zhengzheng Zhai, and Leo Radzihovsky. «Crystal-to-Fracton Tensor Gauge Theory Dualities».Phys. Rev. B100.13 (2019), p. 134113.doi: 10. 1103/PhysRevB.100.134113. arXiv:1907.12577 [cond-mat.str-el]

2019 arXiv
[204]

Gravitoelectromagnetism:ABriefReview .2008.arXiv: gr-qc/ 0311030 [gr-qc]

BahramMashhoon. Gravitoelectromagnetism:ABriefReview .2008.arXiv: gr-qc/ 0311030 [gr-qc]

2008
[205]

«Torsion-inducedgravitational θtermandgravitoelectromagnetism»

Athanasios Chatzistavrakidis, Georgios Karagiannis, and Peter Schupp. «Torsion-inducedgravitational θtermandgravitoelectromagnetism». Eur.Phys. J. C80.11 (2020), p. 1034.doi: 10 . 1140 / epjc / s10052 - 020 - 08600 - 9. arXiv: 2007.06632 [gr-qc]

2020 arXiv
[206]

«Emergent Gravity at a Lifshitz Point from a Bose LiquidontheLattice»

Cenke Xu and Petr Horava. «Emergent Gravity at a Lifshitz Point from a Bose LiquidontheLattice». Phys.Rev.D 81(2010),p.104033. doi: 10.1103/PhysRevD. 81.104033. arXiv:1003.0009 [hep-th]

2010 arXiv
[207]

Barbara M. Terhal. «Quantum error correction for quantum memories».Rev. Mod. Phys.87 (2 2015), pp. 307–346.doi: 10 . 1103 / RevModPhys . 87 . 307. url: https://link.aps.org/doi/10.1103/RevModPhys.87.307

2015 doi
[208]

Han Ma, A. T. Schmitz, S. A. Parameswaran, Michael Hermele, and Rahul M. Nandkishore.«TopologicalEntanglementEntropyofFractonStabilizerCodes». Phys. Rev. B97.12 (2018), p. 125101.doi: 10.1103/PhysRevB.97.125101. arXiv: 1710.01744 [cond-mat.str-el]

2018 arXiv
[209]

arXiv:gr-qc/0606100

Zheng-ChengGuandXiao-GangWen.«ALatticebosonicmodelasaquantum theory of gravity» (June 2006). arXiv:gr-qc/0606100

2006 arXiv
[210]

A. Zee. «GRAVITOMAGNETIC POLE AND MASS QUANTIZATION».Phys. Rev. Lett.55 (1985). [Erratum: Phys.Rev.Lett. 56, 1101 (1986)], pp. 2379–2381. doi: 10.1103/PhysRevLett.55.2379

1985 doi
[211]

«Theoretical Aspects of Massive Gravity».Rev

Kurt Hinterbichler. «Theoretical Aspects of Massive Gravity».Rev. Mod. Phys. 84 (2012), pp. 671–710.doi: 10 . 1103 / RevModPhys . 84 . 671. arXiv: 1105 . 3735 [hep-th]

2012
[212]

R. D. Peccei and Helen R. Quinn. «CP Conservation in the Presence of Instan- tons».Phys. Rev. Lett.38 (1977), pp. 1440–1443.doi: 10.1103/PhysRevLett.38. 1440

1977 doi
[213]

R. D. Peccei and Helen R. Quinn. «Constraints Imposed by CP Conservation in the Presence of Instantons».Phys. Rev. D16 (1977), pp. 1791–1797.doi: 10. 1103/PhysRevD.16.1791. 186 bibliography

1977
[214]

Phys.Rev.Lett

P.Sikivie.«ExperimentalTestsoftheInvisibleAxion». Phys.Rev.Lett. 51(1983). Ed.byM.A.Srednicki.[Erratum:Phys.Rev.Lett.52,695(1984)],pp.1415–1417. doi: 10.1103/PhysRevLett.51.1415

1983 doi
[215]

«Two Applications of Axion Electrodynamics».Phys

Frank Wilczek. «Two Applications of Axion Electrodynamics».Phys. Rev. Lett. 58 (1987), p. 1799.doi: 10.1103/PhysRevLett.58.1799

1987 doi
[216]

L. D. Landau and E. M. Lifschits.The Classical Theory of Fields. Vol. Volume 2. Course of Theoretical Physics. Oxford: Pergamon Press, 1975.isbn: 978-0-08- 018176-9

1975
[217]

Lect.NotesPhys

R.D.Peccei.«TheStrongCPproblemandaxions». Lect.NotesPhys. 741(2008). Ed.byMarkusKuster,GeorgRaffelt,andBertaBeltran,pp.3–17. doi: 10.1007/ 978-3-540-73518-2 _1. arXiv:hep-ph/0607268

2008 arXiv
[218]

Y.S.WuandA.Zee.«Membranes,HigherHopfMaps,andPhaseInteractions». Phys. Lett. B207 (1988), pp. 39–43.doi: 10.1016/0370-2693(88)90882-9

1988 doi
[219]

«Volume-preservingdiffeomorphismasnonabelianhigher-rankgaugesymme- try»

Yi-Hsien Du, Umang Mehta, Dung Xuan Nguyen, and Dam Thanh Son. «Volume-preservingdiffeomorphismasnonabelianhigher-rankgaugesymme- try». SciPost Phys.12.2 (2022), p. 050.doi: 10.21468/SciPostPhys.12.2.050 . arXiv: 2103.09826 [cond-mat.str-el]

2022 arXiv
[220]

«Massive gravity and Fierz-Pauli theory»

Alberto Blasi and Nicola Maggiore. «Massive gravity and Fierz-Pauli theory». Eur. Phys. J. C77.9 (2017), p. 614.doi: 10 . 1140 / epjc / s10052 - 017 - 5205 - y. arXiv: 1706.08140 [hep-th]

2017 arXiv
[221]

«Massive deformations of rank-2 symmet- ric tensor theory (a.k.a

Alberto Blasi and Nicola Maggiore. «Massive deformations of rank-2 symmet- ric tensor theory (a.k.a. BRS characterization of Fierz–Pauli massive gravity)». Class. Quant. Grav.34.1 (2017), p. 015005.doi: 10 . 1088 / 1361 - 6382 / 34 / 1 / 015005. arXiv:1512.01025 [hep-th]

2017 arXiv
[222]

G.BaymandG.Grinstein.«PhaseTransitionintheSigmaModelatFiniteTem- perature». Phys. Rev. D15 (1977), pp. 2897–2912.doi: 10.1103/PhysRevD.15. 2897

1977 doi
[223]

Grater and C

M. Grater and C. Wetterich. «Kosterlitz-Thouless phase transition in the two- dimensional linear sigma model».Phys. Rev. Lett.75 (1995), pp. 378–381.doi: 10.1103/PhysRevLett.75.378. arXiv:hep-ph/9409459

1995 arXiv
[224]

«A note on harmonic gauge(s) in mas- sive gravity».Phys

Giulio Gambuti and Nicola Maggiore. «A note on harmonic gauge(s) in mas- sive gravity».Phys. Lett. B807 (2020), p. 135530.doi: 10 . 1016 / j . physletb . 2020.135530. arXiv:2006.04360 [gr-qc]

2020
[225]

«Fierz–Pauli theory reloaded: from a theory of a symmetric tensor field to linearized massive gravity».Eur

Giulio Gambuti and Nicola Maggiore. «Fierz–Pauli theory reloaded: from a theory of a symmetric tensor field to linearized massive gravity».Eur. Phys. J. C 81.2 (2021), p. 171.doi: 10.1140/epjc/s10052- 021- 08962- 8 . arXiv: 2102. 10813 [gr-qc]

2021 doi
[226]

Cabibbo and G

N. Cabibbo and G. Parisi. «Exponential Hadronic Spectrum and Quark Libera- tion». Phys. Lett. B59 (1975), pp. 67–69.doi: 10.1016/0370-2693(75)90158-6

1975 doi
[227]

Adam Miklos Halasz, A. D. Jackson, R. E. Shrock, Misha A. Stephanov, and J. J. M. Verbaarschot. «On the phase diagram of QCD».Phys. Rev. D58 (1998), p. 096007.doi: 10.1103/PhysRevD.58.096007. arXiv:hep-ph/9804290. bibliography 187

1998 arXiv
[228]

Can.J.Math

PaulA.M.Dirac.«GeneralizedHamiltoniandynamics». Can.J.Math. 2(1950), pp. 129–148.doi: 10.4153/CJM-1950-012-1

1950 doi
[229]

D.DalmaziandR.R.LinodosSantos.«Thedimensionalreductionoflinearized spin-2 theories invariant under transverse diffeomorphisms».Eur. Phys. J. C 81.6 (2021), p. 547.doi: 10 . 1140 / epjc / s10052 - 021 - 09297 - 0. arXiv: 2010 . 12051 [hep-th]

2021
[230]

«Duality in linearized gravity».Phys

Marc Henneaux and Claudio Teitelboim. «Duality in linearized gravity».Phys. Rev. D71 (2005), p. 024018.doi: 10 . 1103 / PhysRevD . 71 . 024018. arXiv: gr - qc/0408101

2005
[231]

«Gravitational Electric- Magnetic Duality, Gauge Invariance and Twisted Self-Duality».J

Claudio Bunster, Marc Henneaux, and Sergio Hortner. «Gravitational Electric- Magnetic Duality, Gauge Invariance and Twisted Self-Duality».J. Phys. A46 (2013). [Erratum: J.Phys.A 46, 269501 (2013)], p. 214016.doi: 10.1088/1751- 8113/46/21/214016. arXiv:1207.1840 [hep-th]

2013 arXiv
[232]

Hofman and Nabil Iqbal

Diego M. Hofman and Nabil Iqbal. «Goldstone modes and photonization for higher form symmetries». SciPost Phys. 6.1 (2019), p. 006. doi: 10 . 21468 / SciPostPhys.6.1.006. arXiv:1802.09512 [hep-th]

2019 arXiv
[233]

Hofman, Austin Joyce, and Grégoire Mathys

Kurt Hinterbichler, Diego M. Hofman, Austin Joyce, and Grégoire Mathys. «Gravity as a gapless phase and biform symmetries».JHEP 02 (2023), p. 151. doi: 10.1007/JHEP02(2023)151. arXiv:2205.12272 [hep-th]

2023 arXiv
[234]

D.Boito,L.N.S.deAndrade,G.deSousa,R.Gama,andC.Y.M.London.«On Maxwell’s electrodynamics in two spatial dimensions».Rev. Bras. Ens. Fis.42 (2020), e20190323. doi: 10 . 1590 / 1806 - 9126 - RBEF - 2019 - 0323. arXiv: 1809 . 07368 [physics.class-ph]

2020
[235]

«Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)d»

Clay Córdova, Po-Shen Hsin, and Nathan Seiberg. «Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)d». SciPost Phys.5.1 (2018), p. 006.doi: 10. 21468/SciPostPhys.5.1.006. arXiv:1712.08639 [cond-mat.str-el]. 188 bibliography

2018 arXiv
[236]

Aragone and A

C. Aragone and A. Khoudeir. «Selfdual massive gravity».Phys. Lett. B173 (1986), pp. 141–144.doi: 10.1016/0370-2693(86)90234-0

1986 doi
[237]

Dalmazi and Elias L

D. Dalmazi and Elias L. Mendonca. «Dual descriptions of spin two massive particles in D=2+1 via master actions».Phys. Rev. D79 (2009), p. 045025.doi: 10.1103/PhysRevD.79.045025. arXiv:0812.0161 [hep-th]

2009 arXiv
[238]

McCarthy

Stanley Deser and James G. McCarthy. «Selfdual formulations of D=3 gravity theories». Phys. Lett. B246 (1990). [Addendum: Phys.Lett.B 248, 473 (1990)], pp. 441–444.doi: 10.1016/0370-2693(90)90627-I

1990 doi
[239]

«Chiral Topological Elasticity and Fracton Order».Phys

Andrey Gromov. «Chiral Topological Elasticity and Fracton Order».Phys. Rev. Lett. 122.7 (2019), p. 076403.doi: 10 . 1103 / PhysRevLett . 122 . 076403. arXiv: 1712.06600 [cond-mat.str-el]

2019 arXiv
[240]

«Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies».Commun

MaissamBarkeshli,ParsaBonderson,Chao-MingJian,MengCheng,andKevin Walker. «Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies».Commun. Math. Phys.374.2 (2019), pp. 1021–1124.doi: 10.1007/s00220- 0...

2019 arXiv
[241]

«DecoratedZ2 symmetrydefectsandtheirtime-reversalanomalies»

Clay Córdova, Kantaro Ohmori, Shu-Heng Shao, and Fei Yan. «DecoratedZ2 symmetrydefectsandtheirtime-reversalanomalies». Phys.Rev.D 102.4(2020), p. 045019.doi: 10.1103/PhysRevD.102.045019. arXiv:1910.14046 [hep-th]

2020 arXiv
[242]

«Theta,TimeReversal,andTemperature»

Davide Gaiotto, Anton Kapustin, Zohar Komargodski, and Nathan Seiberg. «Theta,TimeReversal,andTemperature». JHEP05(2017),p.091. doi: 10.1007/ JHEP05(2017)091. arXiv:1703.00501 [hep-th]

2017 arXiv
[243]

«Comments on global symmetries, anomalies, and duality in (2 + 1)d».JHEP 04 (2017), p

Francesco Benini, Po-Shen Hsin, and Nathan Seiberg. «Comments on global symmetries, anomalies, and duality in (2 + 1)d».JHEP 04 (2017), p. 135.doi: 10.1007/JHEP04(2017)135. arXiv:1702.07035 [cond-mat.str-el]

2017 arXiv
[244]

142.doi: 10.1007/JHEP11(2021)142

DiegoDelmastro,DavideGaiotto,andJaumeGomis.«Globalanomaliesonthe Hilbert space».JHEP 11 (2021), p. 142.doi: 10.1007/JHEP11(2021)142. arXiv: 2101.02218 [hep-th]

2021 arXiv
[245]

«Fermionic Symmetry Protected Topological Phases and Cobordisms».JHEP 12 (2015), p

Anton Kapustin, Ryan Thorngren, Alex Turzillo, and Zitao Wang. «Fermionic Symmetry Protected Topological Phases and Cobordisms».JHEP 12 (2015), p. 052.doi: 10.1007/JHEP12(2015)052. arXiv:1406.7329 [cond-mat.str-el]

2015 arXiv
[246]

J.M.Luttinger.«AnExactlySolubleModelofaMany-FermionSystem». J.Math. Phys.4 (1963), pp. 1154–1162.doi: 10.1063/1.1704046

1963 doi
[247]

«Infrared photons and gravitons»

Steven Weinberg. «Infrared photons and gravitons». Phys. Rev. 140 (1965), B516–B524. doi: 10.1103/PhysRev.140.B516

1965 doi
[248]

Mauro Cirio, Giandomenico Palumbo, and Jiannis K. Pachos. «(3+1) - dimensional topological quantum field theory from a tight-binding model of interactingspinlessfermions». Phys.Rev.B 90.8(2014),p.085114. doi: 10.1103/ PhysRevB.90.085114. arXiv:1309.2380 [cond-mat.str-el]

2014 arXiv
[249]

Chamseddine and M

Ali H. Chamseddine and M. Reuter. «Induced Two-dimensional Quantum Gravity and Sl(2,r) Kac-Moody Current Algebra».Nucl. Phys. B317 (1989), pp. 757–771.doi: 10.1016/0550-3213(89)90542-7

1989 doi
[250]

«Kac-Moody algebras in gravity and M-theories».AIP Conf

Laurent Houart. «Kac-Moody algebras in gravity and M-theories».AIP Conf. Proc. 841.1 (2006). Ed. by Lysiane Mornas and Joaquin Diaz Alonso, pp. 298–

2006
[251]

Phys.Lett

StevenWeinbergandEdwardWitten.«LimitsonMasslessParticles». Phys.Lett. B 96 (1980), pp. 59–62.doi: 10.1016/0370-2693(80)90212-9

1980 doi
[252]

Tomonaga

S. Tomonaga. «Remarks on Bloch’s Method of Sound Waves applied to Many- Fermion Problems».Prog. Theor. Phys.5 (1950), pp. 544–569.doi: 10.1143/PTP. 5.544

1950 doi
[253]

DmitriV.Vassilevich.«Spectralproblemsfromquantumfieldtheory». Contemp. Math.366 (2005), pp. 3–22. arXiv:math-ph/0403052

2005 arXiv
[254]

«Lecture Notes on General Relativity»

M Blau. «Lecture Notes on General Relativity». 2021.url: http://www.blau. itp.unibe.ch/newlecturesGR.pdf

2021
[255]

JHEP05(2015),p.151

TempleHe,VyacheslavLysov,PraharMitra,andAndrewStrominger.«BMSsu- pertranslationsandWeinberg’ssoftgravitontheorem». JHEP05(2015),p.151. doi: 10.1007/JHEP05(2015)151. arXiv:1401.7026 [hep-th]

2015 arXiv
[256]

«Higher-dimensionalsupertranslationsandWeinberg’ssoftgravitontheorem»

Daniel Kapec, Vyacheslav Lysov, Sabrina Pasterski, and Andrew Strominger. «Higher-dimensionalsupertranslationsandWeinberg’ssoftgravitontheorem». Ann. Math. Sci. Appl.02 (2017), pp. 69–94.doi: 10.4310/AMSA.2017.v2.n1.a2 . arXiv: 1502.07644 [gr-qc]. bibliography 189

2017 arXiv
[257]

Misner, K

Charles W. Misner, K. S. Thorne, and J. A. Wheeler.Gravitation. San Francisco: W. H. Freeman, 1973.isbn: 978-0-7167-0344-0, 978-0-691-17779-3

1973
[259]

«The Motion of point particles in curved spacetime».Living Rev

Eric Poisson, Adam Pound, and Ian Vega. «The Motion of point particles in curved spacetime».Living Rev. Rel.14 (2011), p. 7.doi: 10.12942/lrr-2011-7. arXiv: 1102.0529 [gr-qc]

2011 arXiv
[262]

TaichiroKugoandNobuyoshiOhta.«CovariantApproachtotheNo-ghostThe- orem in Massive Gravity».PTEP 2014 (2014), 043B04. doi: 10 . 1093 / ptep / ptu046. arXiv:1401.3873 [hep-th]. 190 bibliography

2014 arXiv
[287]

184 bibliography

doi: 10.1016/0370-2693(79)90838-4. 184 bibliography

doi
[305]

arXiv:hep-th/0511009

doi: 10.1063/1.2218185. arXiv:hep-th/0511009

arXiv
[2011]

doi: 10.1017/cbo9780511973765

doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

«Holographic Projection of Electro- magnetic Maxwell Theory»

Erica Bertolini and Nicola Maggiore. «Holographic Projection of Electro- magnetic Maxwell Theory». Symmetry 12.7 (2020), p. 1134. doi: 10 . 3390 / sym12071134. arXiv:2006.14902 [hep-th]

arXiv 2020

[2] [2]

«Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory».Phys

Erica Bertolini, Giulio Gambuti, and Nicola Maggiore. «Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory».Phys. Rev. D 104.10 (2021), p. 105011.doi: 10 . 1103 / PhysRevD . 104 . 105011. arXiv: 2110 . 13203 [hep-th]

2021

[3] [3]

675.doi: 10

EricaBertolini,FilippoFecit,andNicolaMaggiore.«TopologicalBFDescription of 2D Accelerated Chiral Edge Modes».Symmetry 14.4 (2022), p. 675.doi: 10. 3390/sym14040675. arXiv:2203.13520 [hep-th]

arXiv 2022

[4] [4]

«Maxwell theory of fractons».Phys

Erica Bertolini and Nicola Maggiore. «Maxwell theory of fractons».Phys. Rev. D 106.12 (2022), p. 125008.doi: 10.1103/PhysRevD.106.125008 . arXiv:2209. 01485 [hep-th]

doi:10.1103/physrevd.106.125008 2022

[5] [5]

«Gaug- ing Fractons and Linearized Gravity».Symmetry 15.4 (2023), p

Erica Bertolini, Alberto Blasi, Andrea Damonte, and Nicola Maggiore. «Gaug- ing Fractons and Linearized Gravity».Symmetry 15.4 (2023), p. 945.doi: 10 . 3390/sym15040945. arXiv:2304.10789 [hep-th]

arXiv 2023

[6] [6]

EricaBertolini,NicolaMaggiore,andGiandomenicoPalumbo.«Covariantfrac- ton gauge theory with boundary».Phys. Rev. D108.2 (2023), p. 025009.doi: 10.1103/PhysRevD.108.025009. arXiv:2306.13883 [hep-th]

arXiv 2023

[7] [7]

«Theory of a symmetric tensor field with boundary: Kac-Moody algebras in linearized gravity».Phys

Erica Bertolini and Nicola Maggiore. «Theory of a symmetric tensor field with boundary: Kac-Moody algebras in linearized gravity».Phys. Rev. D 108.10 (2023), p. 105012.doi: 10 . 1103 / PhysRevD . 108 . 105012. arXiv: 2310 . 20303 [hep-th]

2023

[8] [8]

H. B. G. Casimir. «On the attraction between two perfectly conducting plates». Indag. Math.10.4 (1948), pp. 261–263

1948