Pith. sign in

REVIEW 5 major objections 3 minor 2 cited by

Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory

T0 review · 5 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper constructs an explicit conformal map between the state and operator pictures of (2+1)-dimensional non-Lorentzian CFTs with SU(1,2)$\times$U(1) symmetry, and derives the resulting Hamiltonian identity.

desk verdict New state-picture TNC construction, but the central conformal map is internally inconsistent as printed. read the letter →

arxiv 2411.11951 v3 pith:BIK6PHEI submitted 2024-11-18 hep-th

Stefano Baiguera , Troels Harmark , Yang Lei , Ziqi Yan This is my paper · ORCID
classification hep-th
keywords non-Lorentzianconformalfieldtheorystate-operatorcorrespondencetorsionalNewton-CartangeometrynullreductionOmega-deformationSU(12)symmetryLifshitzscalingSpinMatrix
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 paper aims to establish a state-operator correspondence in a class of (2+1)-dimensional non-Lorentzian conformal field theories whose symmetry group is SU(1,2)$\times$U(1). It builds the state picture by null-reducing the Lorentzian cylinder $\mathbb{R}\times S^3$, producing a torsional Newton-Cartan geometry, and the operator picture by taking an infinite-radius limit, which yields an $\Omega$-deformed TNC geometry. The main result is an explicit conformal mapping between these geometries, under which the state-picture Hamiltonian becomes $H_0 = \tfrac12(R^2 H + C/R^2 - J - N)$ in operator-picture generators. This matters because it gives one of the first geometric, rather than purely algebraic, realizations of the state-operator correspondence for SU(1,2) non-Lorentzian CFTs, with direct relevance to near-BPS sectors of $\mathcal{N}=4$ super-Yang-Mills and to non-Lorentzian holography.

What carries the argument

The load-bearing object is torsional Newton-Cartan (TNC) geometry, a trio of fields $(\tau_\mu, h_{\mu\nu}, m_\mu)$ that describes a non-Lorentzian spacetime after null reduction: $\tau_\mu$ is the clock one-form, $h_{\mu\nu}$ the spatial metric, and $m_\mu$ a U(1) gauge field. The conformal mapping is derived by solving the Weyl condition $ds^2=\Omega^2 d\hat{s}^2$ between the parent four-dimensional null-reduced metrics, with the ansatz that both the null direction and the angular coordinate are identified. This reduces the problem to a pair of decoupled second-order PDEs whose unique, up to Lifshitz rescaling, real solution is the map in Eqs. (3.24) and (4.22). The same map then carries the generators of su(1,2)$\oplus$u(1) between the two pictures.

What would settle it

A free-field computation would settle the claim: null-reduce a free complex scalar on $\mathbb{R}\times S^3$ at fixed null momentum $P_u=E-S$, compute the spectrum of $H_0=\partial_{x_0}$ in the state picture, and compare with the scaling dimensions of operators at the origin of the $\Omega$-deformed picture using Eq. (3.31); any mismatch in the descendant tower would show the map does not implement the correspondence.

Watch

Extended reading notes

Core claim

The central claim is that the two non-Lorentzian geometries, namely the state-picture TNC background obtained by null reduction of $\mathbb{R}\times S^3$ and the operator-picture $\Omega$-deformed TNC background, are related by an exact conformal transformation given in Eqs. (3.24) and (4.22). The map preserves the null isometry, fixes the U(1) particle-number generator, and transforms the Hamiltonian $H_0=\partial_{x_0}$, which defines equal-time evolution in the state picture, into $H_0=\tfrac12(R^2H+C/R^2-J-N)$, where $H$, $C$, $J$, and $N$ are respectively the Hamiltonian, special conformal generator, angular momentum, and particle-number generator of the operator picture. The paper further shows that constant-$x_0$ slices map to the quartic surfaces $(t-a)^2+r^4=1+a^2$, reflecting the z=2 Lifshitz scaling. This is presented as the geometric counterpart of earlier algebraic constructions of the state-operator correspondence for SU(1,n) theories.

Load-bearing premise

The load-bearing premise is that x0 is a legitimate global time coordinate for defining the state-picture Hilbert space despite the spacetime's twisted clock one-form; if x0 is not valid, the Hamiltonian and the whole correspondence are ill-defined.

Editorial extensions

If this is right

  • The state-picture Hamiltonian $H_0=\partial_{x_0}$ is identified with the operator-picture combination $\tfrac12(R^2H+C/R^2-J-N)$, so eigenvalues of $H_0$ on primary states give scaling dimensions, up to constant shifts from $J$ and $N$.
  • The operator-picture $\Omega$-deformed geometry is obtained as the infinite-radius limit of the state-picture geometry, making the two descriptions of SU(1,2) CFTs manifestly equivalent.
  • The conformal map preserves the null translation, so the U(1) particle-number charge is identical in both pictures, which is what allows the null reduction to be performed consistently.
  • Constant-time slices in the state picture become the quartic curves $(t-a)^2+r^4=1+a^2$; for $r<1$ these define a foliation with well-defined causality, while outside that region the twist torsion of the TNC geometry makes the slicing non-foliating.
  • This geometric map supplies the missing state-picture geometry for SU(1,2) CFTs and extends the algebraic state-operator correspondence of earlier work to a concrete coordinate transformation.

Reading between the lines

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

  • A direct testable consequence, which the paper does not carry out, is that a free-field or free-fermion realization of an SU(1,2)$\times$U(1) CFT on the $\Omega$-deformed background should reproduce the state-picture spectrum through Eq. (3.31).
  • The construction suggests that an analogous conformal map should exist for the superconformal extension PSU(1,2$|$3), which would provide a geometric setting for Spin Matrix Theory; the paper leaves this extension implicit.
  • Because the constant-time surfaces are closed and intersect for large $r$, the state-operator correspondence may only be globally defined on the region $r<1$ where the causal structure is well behaved, a restriction the paper notes but does not resolve.
  • The uniqueness of the solution to the constraint equations, up to Lifshitz rescaling, hints that the conformal map between the two pictures is rigid, so any SU(1,2)-invariant state-operator correspondence must reduce to this one; this uniqueness goes beyond what the paper explicitly claims.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 3 minor

Summary. The paper proposes a state-operator correspondence for (2+1)-dimensional non-Lorentzian CFTs with SU(1,2)×U(1) symmetry. The state picture is obtained by null reducing the Lorentzian cylinder R×S^3, producing the TNC data (3.8); the operator picture is obtained by an infinite-radius limit with a z=2 rescaling, giving the Ω-deformed TNC geometry (3.19)/(3.23). The central claim is an explicit conformal map, quoted as Eqs. (3.24) and derived again as Eqs. (4.22), together with the generator identity H0 = (1/2)(R^2 H + C/R^2 - J - N) in Eq. (3.31). If correct, this would be a concrete geometric realization of the non-Lorentzian state-operator correspondence. The derivation strategy is self-contained and uses no fitted parameters, but the central formulas as printed are internally inconsistent.

Significance. The approach is potentially valuable: a null-reduction derivation of the state-picture TNC geometry, an independent infinite-radius limit giving the operator-picture Ω-deformed geometry, and a PDE-based derivation of the conformal map would place the algebraic state-operator correspondence of Lambert et al. on a geometric footing. The paper also honestly flags the twist-torsion issue in Section 3.1. However, the main deliverables—the explicit map and the resulting Hamiltonian identity—are not internally consistent as printed. Since the paper's central contribution is precisely that map, the inconsistency affects the validity of the main claim rather than being a presentation issue.

major comments (5)
  1. [§3.3, Eqs. (3.22)–(3.23)] The displayed polar-coordinate transformation is not compatible with the claimed operator-picture geometry. Substituting x = 2r cos φ, y = 2r sin φ, T = t/2 - r² sin(2φ) into τ = dT + x dy - y dx in Eq. (3.19) gives τ = (1/2)dt - 2r sin(2φ) dr + (4r² - 2r² cos(2φ)) dφ, not the 2dt + 4r² dφ of Eq. (3.23). The operator-picture target geometry used in the conformal mapping is therefore not the polar form of Eq. (3.19) as printed.
  2. [§4.1, Eq. (4.5) vs Eq. (3.23)] The operator-picture TNC data used in the derivation are not those displayed in Section 3. Eq. (4.5) states τ̂ = d t̂ + r̂² dφ̂ and m̂ = (1/2)dφ̂, whereas Eq. (3.23) states τ̂ = 2 d t̂ + 4 r̂² dφ̂ and m̂ = 0. The stated redefinition u = û + φ̂/2 does not change τ or h and only shifts m, so it cannot convert Eq. (3.23) into Eq. (4.5) unless an additional coordinate rescaling is silently introduced. Since Section 4 solves for the map to Eq. (4.5), its result (4.22) cannot be quoted as the map to Eq. (3.23).
  3. [§3.4 and §4.2, Eqs. (3.24) and (4.22)] The conformal map (3.24) is not obtained from the derived solution (4.22). Using X0 = x0 - φ/2 and Θ = θ/2, Eq. (4.22a) gives x0 + φ/2 = X0 + φ = -arccot((t²+r⁴-1)/(2t)) + φ̂ - arctan((r²-1)/t), while Eq. (3.24a) omits the φ̂ - arctan term and has the arccot argument without the factor 2. Similarly, combining Θ = θ/2 with the second equation of (4.22a) gives cos θ = (t²+r⁴-6r²+1)/(t²+(r²+1)²), whereas Eq. (3.24c) prints (1-8r²)/(t²+(r²+1)²). These are different functions, not typographical variants.
  4. [§3.5, Eqs. (3.31), (3.45), (5.1)] The central generator identity is stated with conflicting normalizations. Eq. (3.31) reads H0 = (1/2)(R²H + C/R² - J - N), Eq. (3.45) reads H0 = R²H + C/R² - J - m, and Eq. (5.1) uses -i/2(R²H + C/R² - J - m). As written, these cannot all be true simultaneously unless m is tied to N by an unstated factor of two. Because this identity is the main physical result, the normalization must be fixed and re-derived from a consistent map.
  5. [§3.1 and §3.5.1] The paper asserts in Section 3.1 that x0 is a globally well-defined time coordinate even though the temporal vielbein (3.8) has non-vanishing twist torsion (τ∧dτ ≠ 0), and Section 3.5.1 observes that constant-x0 surfaces map to closed curves (3.32) that do not foliate the operator geometry for r > 1. If the Hilbert space is to be built on equal-time slices x0 = const, the absence of a global foliation needs to be addressed; the statement that x0 is globally well-defined is not by itself sufficient, since the TNC time evolution is determined by the non-closed one-form τ.
minor comments (3)
  1. [§4.2, after Eq. (4.22)] The text says r ≡ r̂/R 'as defined in Eq. (3.25)', but Eq. (3.25) defines r ≡ r̂/(2R). This factor-of-two discrepancy propagates into the comparison of (4.22) with (3.24).
  2. [§3.4, after Eq. (3.26)] The sentence 'Using the first equation in Eq. (3.24c)' appears to refer to Eq. (3.24b); Eq. (3.24c) has only one displayed equation.
  3. [§4.1, Eq. (4.4)] The symbol u is reused for both the state-picture and operator-picture null coordinates in Eqs. (3.26) and (4.4). This is confusing and likely contributed to the sign and factor inconsistencies between Sections 3 and 4.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the conformal map is derived by solving PDEs and the generator identity follows by substitution; cited prior work is corroborative, not load-bearing.

full rationale

I walked the derivation chain. The central conformal map is obtained by solving the Weyl condition (4.14) for the explicitly stated ansatz (4.11), leading to the differential equations (4.15), the general solution (4.19), and the forced linearity of D1 and D2 via (4.21). No parameter is fitted to the target identity (3.31); the generator identity is obtained by substituting the map into H0 = ∂x0 and comparing with the independently defined operator-picture differential generators (3.30). The operator-picture geometry is first derived by an R → ∞ limit of the state-picture TNC data in Section 3.3, Eqs. (3.17)-(3.19), and then noted to match Lambert et al.; even if one imported [1], it is external work without overlapping authors and is corroborated by the paper's own null-reduction calculation. The algebraic state-operator material from [20] and [1] is used for interpretation, not to fix the geometric map. Choices such as Pu = E − S and x0 as global time are stated assumptions or construction choices, not outputs of the derivation. The skeptical objection about mismatches between (3.22) and (3.23), or between (3.24) and (4.22), concerns internal mathematical consistency rather than circularity: it does not make the derivation reduce to its own inputs. Self-citations appear mainly in the introduction and discussion as motivation, not as load-bearing evidence for the conformal map. I therefore find no significant circularity.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No new particles or fields are introduced. The paper's assumptions are the standard null-reduction dictionary plus two modeling choices: the specific null momentum Pu = E - S and the specific infinite-radius scaling. The isometry-preservation constraints are stated explicitly as part of the derivation.

free parameters (1)
  • null reduction mixing parameter alpha = 0
    Eq (3.5) sets the null momentum as Pu = E - S, corresponding to the choice alpha = 0 in the family E + alpha S = partial_x0 mentioned in footnote 8. This is a hand-chosen value that determines the state-picture geometry and the preserved subalgebra; other alpha would give different non-Lorentzian CFTs.
assumptions (5)
  • domain assumption Null reduction of a relativistic CFT on R times S^3 with fixed null momentum produces a non-Lorentzian CFT with Bargmann mass equal to Pu.
    Invoked in Section 3.1 after Eq (3.7); this is the standard null-reduction technique cited to [1,21,45-48,55,67-80].
  • domain assumption The centralizer of Pu = E - S inside so(2,4) is su(1,2), and this identifies the non-Lorentzian conformal group.
    Stated in Section 3.1 as the first motivation for the choice Pu = E - S and analyzed in Section 3.2.
  • domain assumption The temporal coordinate x0 is globally well-defined and can serve as the Hamiltonian time despite the twistless torsion (d tau different from 0, tau wedge d tau different from 0).
    Discussed at the end of Section 3.1: 'x0 (instead of tau) is a globally well-defined time coordinate'; this is essential for defining H0 = partial_x0 in Eq (3.28).
  • ad hoc to paper The conformal map between state and operator pictures preserves both the null isometry partial_u = partial_u and the angular isometry partial_phi = partial_phi_hat.
    Imposed in Section 4.1, Eqs (4.7) and (4.9); these constraints restrict the coordinate transformation and are necessary for the null-reduction interpretation, but are not derived from first principles.
  • ad hoc to paper The operator picture is obtained from the infinite-radius limit with the z=2 rescaling x0 = T/R^2, which keeps the TNC data finite.
    Eq (3.17) in Section 3.3; this is a non-naive limit chosen to produce a non-singular geometry, and it yields the Omega-deformed background matching [1].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory." pith.science (2026). https://pith.science/paper/BIK6PHEI

@misc{pith2026241111951,
  author       = {Pith},
  title        = {Pith review of: Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BIK6PHEI}},
  note         = {Machine review of arXiv:2411.11951}
}
abstract

We realize an explicit conformal mapping between the state and operator pictures in a class of (2+1)-dimensional non-Lorentzian field theories with SU(1,2)$\times$U(1) conformal symmetry. The state picture arises from null reducing four-dimensional relativistic conformal field theories on a three-sphere, yielding a non-Lorentzian geometry with the conformal Killing symmetry group SU(1,2). This is complementary to the operator picture recently studied by Lambert et al., where the geometry acquires an $\Omega$-deformation. We then use the geometric mapping between the two pictures to derive a correspondence between the generators. This provides a concrete realization of the state-operator correspondence in non-Lorentzian conformal field theories.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Revisiting Schr\"odinger CFTs: Factorization, Massless Particles, and a Path to the Bootstrap

    hep-th 2025-10 conditional novelty 7.0 of 10

    Schrödinger CFTs are reformulated via a harmonic-trap thermofield double, giving a state-operator correspondence for all operators and a factorization proof of non-renormalization.

  2. An Introduction to String Newton-Cartan Holography and Integrability

    hep-th 2026-03 accept novelty 3.0 of 10

    String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.

Reference graph

Works this paper leans on

125 extracted references · 17 canonical work pages · cited by 2 Pith papers

  1. [1]

    Lambert, R

    N. Lambert, R. Mouland and T. Orchard, Non-Lorentzian SU(1, n) Spacetime Symmetry In Various Dimensions, Front. in Phys. 10 (2022) 864800 [ 2112.14860]

    arXiv 2022

  2. [2]

    Coleman and A

    P. Coleman and A. J. Schofield, Quantum criticality, Nature 433 (2005) 226

    2005

  3. [3]

    Sachdev, Quantum Phase Transitions

    S. Sachdev, Quantum Phase Transitions. Cambridge University Press, 2 ed., 2011

    2011

  4. [4]

    Sachdev and B

    S. Sachdev and B. Keimer, Quantum Criticality, Phys. Today 64N2 (2011) 29 [ 1102.4628]

    arXiv 2011

  5. [5]

    Hoyos, B

    C. Hoyos, B. S. Kim and Y. Oz, Lifshitz Hydrodynamics, JHEP 11 (2013) 145 [ 1304.7481]

    arXiv 2013

  6. [6]

    Hoyos, B

    C. Hoyos, B. S. Kim and Y. Oz, Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity, JHEP 03 (2014) 029 [ 1309.6794]

    arXiv 2014

  7. [7]

    Chapman, C

    S. Chapman, C. Hoyos and Y. Oz, Lifshitz Superfluid Hydrodynamics, JHEP 07 (2014) 027 [1402.2981]

    arXiv 2014

  8. [8]

    Hoˇ rava,Quantum Gravity at a Lifshitz Point , Phys

    P. Hoˇ rava,Quantum Gravity at a Lifshitz Point , Phys. Rev. D 79 (2009) 084008 [ 0901.3775]

    arXiv 2009

Show all 125 references
  1. [9]

    S. A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [ 0912.1061]

    2010 arXiv

  2. [10]

    Kachru, X

    S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points , Phys. Rev. D 78 (2008) 106005 [ 0808.1725]

    2008 arXiv

  3. [11]

    Baiguera, Aspects of non-relativistic quantum field theories , Eur

    S. Baiguera, Aspects of non-relativistic quantum field theories , Eur. Phys. J. C 84 (2024) 268 [2311.00027]

    2024 arXiv

  4. [12]

    Duval, M

    C. Duval, M. Henkel, P. Horvathy, S. Rouhani and P. Zhang, Schr¨ odinger Symmetry: A Historical Review, Int. J. Theor. Phys. 63 (2024) 184 [ 2403.20316]

    2024 arXiv

  5. [13]

    Golkar and D

    S. Golkar and D. T. Son, Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories , JHEP 12 (2014) 063 [ 1408.3629]

    2014 arXiv

  6. [14]

    W. D. Goldberger, Z. U. Khandker and S. Prabhu, OPE convergence in non-relativistic conformal field theories , JHEP 12 (2015) 048 [ 1412.8507]

    2015 arXiv

  7. [15]

    Gubler, N

    P. Gubler, N. Yamamoto, T. Hatsuda and Y. Nishida, Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method , Annals Phys. 356 (2015) 467 [ 1501.06053]. – 33 –

    2015 arXiv

  8. [16]

    Chen, P.-X

    B. Chen, P.-X. Hao, R. Liu and Z.-F. Yu, On Galilean conformal bootstrap, JHEP 06 (2021) 112 [2011.11092]

    2021 arXiv

  9. [17]

    Chen, P.-X

    B. Chen, P.-X. Hao, R. Liu and Z.-F. Yu, On Galilean conformal bootstrap. Part II. ξ = 0 sector, JHEP 12 (2022) 019 [ 2207.01474]

    2022 arXiv

  10. [18]

    D. T. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas , Annals Phys. 321 (2006) 197 [ cond-mat/0509786]

    2006 arXiv

  11. [19]

    Nishida and D

    Y. Nishida and D. T. Son, An Epsilon expansion for Fermi gas at infinite scattering length , Phys. Rev. Lett. 97 (2006) 050403 [ cond-mat/0604500]

    2006 arXiv

  12. [20]

    Nishida and D

    Y. Nishida and D. T. Son, Nonrelativistic conformal field theories , Phys. Rev. D 76 (2007) 086004 [0706.3746]

    2007 arXiv

  13. [21]

    D. T. Son, Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry, Phys. Rev. D 78 (2008) 046003 [ 0804.3972]

    2008 arXiv

  14. [22]

    Nishida and D

    Y. Nishida and D. T. Son, Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories, Lect. Notes Phys. 836 (2012) 233 [ 1004.3597]

    2012 arXiv

  15. [23]

    Bekaert, E

    X. Bekaert, E. Meunier and S. Moroz, Symmetries and currents of the ideal and unitary Fermi gases, JHEP 02 (2012) 113 [ 1111.3656]

    2012 arXiv

  16. [24]

    Raviv-Moshe and S

    A. Raviv-Moshe and S. Zhong, Impurities in Schr¨ odinger field theories and s-wave resonance, 2411.04040

  17. [25]

    D. B. Kaplan, M. J. Savage and M. B. Wise, A New expansion for nucleon-nucleon interactions, Phys. Lett. B 424 (1998) 390 [ nucl-th/9801034]

    1998 arXiv

  18. [26]

    P. F. Bedaque, H. W. Hammer and U. van Kolck, Renormalization of the three-body system with short range interactions , Phys. Rev. Lett. 82 (1999) 463 [ nucl-th/9809025]

    1999 arXiv

  19. [27]

    C. A. Regal, M. Greiner and D. S. Jin, Observation of resonance condensation of fermionic atom pairs, Phys. Rev. Lett. 92 (2004) 040403

    2004

  20. [28]

    M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman and W. Ketterle, Condensation of pairs of fermionic atoms near a feshbach resonance , Phys. Rev. Lett. 92 (2004) 120403

    2004

  21. [29]

    Balasubramanian and J

    K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs , Phys. Rev. Lett. 101 (2008) 061601 [ 0804.4053]

    2008 arXiv

  22. [30]

    Oling and Z

    G. Oling and Z. Yan, Aspects of Nonrelativistic Strings , Front. in Phys. 10 (2022) 832271 [2202.12698]

    2022 arXiv

  23. [31]

    C. D. A. Blair, J. Lahnsteiner, N. A. Obers and Z. Yan, Matrix theory reloaded: a BPS road to holography, JHEP 02 (2025) 024 [ 2410.03591]

    2025 arXiv

  24. [32]

    J. A. Minahan and K. Zarembo, The Bethe ansatz for N=4 superYang-Mills , JHEP 03 (2003) 013 [hep-th/0212208]

    2003 arXiv

  25. [33]

    Beisert, C

    N. Beisert, C. Kristjansen and M. Staudacher, The Dilatation operator of conformal N=4 superYang-Mills theory, Nucl. Phys. B 664 (2003) 131 [ hep-th/0303060]

    2003 arXiv

  26. [34]

    Beisert, The su(2—3) dynamic spin chain , Nucl

    N. Beisert, The su(2—3) dynamic spin chain , Nucl. Phys. B 682 (2004) 487 [hep-th/0310252]. – 34 –

    2004 arXiv

  27. [35]

    Beisert, The Dilatation operator of N=4 super Yang-Mills theory and integrability , Phys

    N. Beisert, The Dilatation operator of N=4 super Yang-Mills theory and integrability , Phys. Rept. 405 (2004) 1 [ hep-th/0407277]

    2004 arXiv

  28. [36]

    Bellucci, P.-Y

    S. Bellucci, P.-Y. Casteill and J. Morales, Superstring sigma models from spin chains: The SU(1,1—1) case, Nucl. Phys. B 729 (2005) 163 [ hep-th/0503159]

    2005 arXiv

  29. [37]

    Bellucci and P.-Y

    S. Bellucci and P.-Y. Casteill, Sigma model from SU(1,1—2) spin chain , Nucl. Phys. B 741 (2006) 297 [ hep-th/0602007]

    2006 arXiv

  30. [38]

    Beisert and B

    N. Beisert and B. I. Zwiebel, On Symmetry Enhancement in the psu(1,1—2) Sector of N=4 SYM, JHEP 10 (2007) 031 [ 0707.1031]

    2007 arXiv

  31. [39]

    B. I. Zwiebel, The psu (1,1—2) Spin Chain of N = 4 Supersymmetric Yang-Mills Theory, Ph.D. thesis, Princeton U., 2007

    2007

  32. [40]

    Beisert, The su(2—3) Undynamic Spin Chain , Prog

    N. Beisert, The su(2—3) Undynamic Spin Chain , Prog. Theor. Phys. Suppl. 177 (2009) 1 [0807.0099]

    2009 arXiv

  33. [41]

    Beisert et al., Review of AdS/CFT Integrability: An Overview , Lett

    N. Beisert et al., Review of AdS/CFT Integrability: An Overview , Lett. Math. Phys. 99 (2012) 3 [1012.3982]

    2012 arXiv

  34. [42]

    D. E. Berenstein, J. M. Maldacena and H. S. Nastase, Strings in flat space and pp waves from N=4 superYang-Mills, JHEP 04 (2002) 013 [ hep-th/0202021]

    2002 arXiv

  35. [43]

    Kruczenski, Spin chains and string theory , Phys

    M. Kruczenski, Spin chains and string theory , Phys. Rev. Lett. 93 (2004) 161602 [hep-th/0311203]

    2004 arXiv

  36. [44]

    Harmark and M

    T. Harmark and M. Orselli, Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence, JHEP 11 (2014) 134 [ 1409.4417]

    2014 arXiv

  37. [45]

    Lambert, A

    N. Lambert, A. Lipstein and P. Richmond, Non-Lorentzian M5-brane Theories from Holography, JHEP 08 (2019) 060 [ 1904.07547]

    2019 arXiv

  38. [46]

    Lambert, A

    N. Lambert, A. Lipstein, R. Mouland and P. Richmond, Bosonic symmetries of (2, 0) DLCQ field theories, JHEP 01 (2020) 166 [ 1912.02638]

    2020 arXiv

  39. [47]

    Lambert and T

    N. Lambert and T. Orchard, Non-Lorentzian Avatars of (1, 0) Theories, JHEP 02 (2021) 205 [2011.06968]

    2021 arXiv

  40. [48]

    Lambert, A

    N. Lambert, A. Lipstein, R. Mouland and P. Richmond, Five-dimensional non-Lorentzian conformal field theories and their relation to six-dimensions , JHEP 03 (2021) 053 [2012.00626]

    2021 arXiv

  41. [49]

    Lambert, A

    N. Lambert, A. Lipstein and R. Mouland, Six-dimensional correlators from a five-dimensional operator product expansion, JHEP 06 (2024) 055 [ 2401.07932]

    2024 arXiv

  42. [50]

    G. K. Karananas and A. Monin, More on the operator-state map in nonrelativistic CFTs , Phys. Rev. D 105 (2022) 065008 [ 2109.03836]

    2022 arXiv

  43. [51]

    M. H. Christensen, J. Hartong, N. A. Obers and B. Rollier, Torsional Newton-Cartan Geometry and Lifshitz Holography , Phys. Rev. D 89 (2014) 061901 [ 1311.4794]

    2014 arXiv

  44. [52]

    M. H. Christensen, J. Hartong, N. A. Obers and B. Rollier, Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography , JHEP 01 (2014) 057 [ 1311.6471]

    2014 arXiv

  45. [53]

    Harmark, K

    T. Harmark, K. R. Kristjansson and M. Orselli, Decoupling limits of N = 4 super Yang-Mills on R × S3, JHEP 09 (2007) 115 [ 0707.1621]. – 35 –

    2007 arXiv

  46. [54]

    Harmark and N

    T. Harmark and N. Wintergerst, Nonrelativistic Corners of N = 4 Supersymmetric Yang–Mills Theory, Phys. Rev. Lett. 124 (2020) 171602 [ 1912.05554]

    2020 arXiv

  47. [55]

    Baiguera, T

    S. Baiguera, T. Harmark and N. Wintergerst, Nonrelativistic near-BPS corners of N = 4 super-Yang-Mills with SU (1, 1) symmetry, JHEP 02 (2021) 188 [ 2009.03799]

    2021 arXiv

  48. [56]

    Baiguera, T

    S. Baiguera, T. Harmark, Y. Lei and N. Wintergerst, Symmetry structure of the interactions in near-BPS corners of N = 4 super-Yang-Mills, JHEP 04 (2021) 029 [ 2012.08532]

    2021 arXiv

  49. [57]

    Baiguera, T

    S. Baiguera, T. Harmark and Y. Lei, Spin Matrix Theory in near 1 8 -BPS corners of N = 4 super-Yang-Mills, JHEP 02 (2022) 191 [ 2111.10149]

    2022 arXiv

  50. [58]

    Baiguera, T

    S. Baiguera, T. Harmark and Y. Lei, The Panorama of Spin Matrix theory , JHEP 04 (2023) 075 [2211.16519]

    2023 arXiv

  51. [59]

    Di Francesco, P

    P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory , Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997, 10.1007/978-1-4612-2256-9

    1997 doi

  52. [60]

    Rychkov, EPFL Lectures on Conformal Field Theory in D >= 3 Dimensions , SpringerBriefs in Physics

    S. Rychkov, EPFL Lectures on Conformal Field Theory in D >= 3 Dimensions , SpringerBriefs in Physics. Springer Cham, 1, 2016, 10.1007/978-3-319-43626-5, [ 1601.05000]

    2016 arXiv

  53. [61]

    Simmons-Duffin, The Conformal Bootstrap , in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings , pp

    D. Simmons-Duffin, The Conformal Bootstrap , in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings , pp. 1–74, 2017, 1602.07982, DOI

    2017 arXiv

  54. [62]

    Belin, J

    A. Belin, J. De Boer and J. Kruthoff, Comments on a state-operator correspondence for the torus, SciPost Phys. 5 (2018) 060 [ 1802.00006]

    2018 arXiv

  55. [63]

    Minwalla, Restrictions imposed by superconformal invariance on quantum field theories , Adv

    S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories , Adv. Theor. Math. Phys. 2 (1998) 783 [ hep-th/9712074]

    1998 arXiv

  56. [64]

    Luscher and G

    M. Luscher and G. Mack, Global Conformal Invariance in Quantum Field Theory , Commun. Math. Phys. 41 (1975) 203

    1975

  57. [65]

    Chagnet, S

    N. Chagnet, S. Chapman, J. de Boer and C. Zukowski, Complexity for Conformal Field Theories in General Dimensions , Phys. Rev. Lett. 128 (2022) 051601 [ 2103.06920]

    2022 arXiv

  58. [66]

    S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity . Cambridge University Press, 7, 2019, 10.1017/9781108770385

    2019 doi

  59. [67]

    Jensen, Anomalies for Galilean fields , SciPost Phys

    K. Jensen, Anomalies for Galilean fields , SciPost Phys. 5 (2018) 005 [ 1412.7750]

    2018 arXiv

  60. [68]

    Jensen, On the coupling of Galilean-invariant field theories to curved spacetime , SciPost Phys

    K. Jensen, On the coupling of Galilean-invariant field theories to curved spacetime , SciPost Phys. 5 (2018) 011 [ 1408.6855]

    2018 arXiv

  61. [69]

    Auzzi, S

    R. Auzzi, S. Baiguera and G. Nardelli, On Newton-Cartan trace anomalies , JHEP 02 (2016) 003 [1511.08150]

    2016 arXiv

  62. [70]

    Auzzi, S

    R. Auzzi, S. Baiguera, F. Filippini and G. Nardelli, On Newton-Cartan local renormalization group and anomalies , JHEP 11 (2016) 163 [ 1610.00123]

    2016 arXiv

  63. [71]

    Auzzi and G

    R. Auzzi and G. Nardelli, Heat kernel for Newton-Cartan trace anomalies , JHEP 07 (2016) 047 [1605.08684]

    2016 arXiv

  64. [72]

    I. Arav, S. Chapman and Y. Oz, Non-Relativistic Scale Anomalies, JHEP 06 (2016) 158 [1601.06795]. – 36 –

    2016 arXiv

  65. [73]

    Festuccia, D

    G. Festuccia, D. Hansen, J. Hartong and N. A. Obers, Symmetries and Couplings of Non-Relativistic Electrodynamics, JHEP 11 (2016) 037 [ 1607.01753]

    2016 arXiv

  66. [74]

    Auzzi, S

    R. Auzzi, S. Baiguera and G. Nardelli, Trace anomaly for non-relativistic fermions , JHEP 08 (2017) 042 [ 1705.02229]

    2017 arXiv

  67. [75]

    Auzzi, S

    R. Auzzi, S. Baiguera and G. Nardelli, Nonrelativistic trace and diffeomorphism anomalies in particle number background, Phys. Rev. D 97 (2018) 085010 [ 1711.00910]

    2018 arXiv

  68. [76]

    Auzzi, S

    R. Auzzi, S. Baiguera, G. Nardelli and S. Penati, Renormalization properties of a Galilean Wess-Zumino model, JHEP 06 (2019) 048 [ 1904.08404]

    2019 arXiv

  69. [77]

    Chapman, L

    S. Chapman, L. Di Pietro, K. T. Grosvenor and Z. Yan, Renormalization of Galilean Electrodynamics, JHEP 10 (2020) 195 [ 2007.03033]

    2020 arXiv

  70. [78]

    Bagchi, R

    A. Bagchi, R. Basu, M. Islam, K. S. Kolekar and A. Mehra, Galilean gauge theories from null reductions, JHEP 04 (2022) 176 [ 2201.12629]

    2022 arXiv

  71. [79]

    Baiguera, L

    S. Baiguera, L. Cederle and S. Penati, Supersymmetric Galilean Electrodynamics, JHEP 09 (2022) 237 [ 2207.06435]

    2022 arXiv

  72. [80]

    Smith, Fermions with SU(1, n) spacetime symmetry , JHEP 11 (2023) 032 [ 2307.16624]

    J. Smith, Fermions with SU(1, n) spacetime symmetry , JHEP 11 (2023) 032 [ 2307.16624]

    2023 arXiv

  73. [81]

    Penrose, Any Space-Time has a Plane Wave as a Limit , pp

    R. Penrose, Any Space-Time has a Plane Wave as a Limit , pp. 271–275. Springer Netherlands, Dordrecht, 1976

    1976

  74. [82]

    M. Blau, J. M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, Penrose limits and maximal supersymmetry, Class. Quant. Grav. 19 (2002) L87 [ hep-th/0201081]

    2002 arXiv

  75. [83]

    Harmark, J

    T. Harmark, J. Hartong, N. A. Obers and G. Oling, Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT , JHEP 03 (2021) 129 [ 2011.02539]

    2021 arXiv

  76. [84]

    Hartong, N

    J. Hartong, N. A. Obers and G. Oling, Review on Non-Relativistic Gravity , Front. in Phys. 11 (2023) 1116888 [ 2212.11309]

    2023 arXiv

  77. [85]

    K. T. Grosvenor, J. Hartong, C. Keeler and N. A. Obers, Homogeneous Nonrelativistic Geometries as Coset Spaces , Class. Quant. Grav. 35 (2018) 175007 [ 1712.03980]

    2018 arXiv

  78. [86]

    Hartong, Y

    J. Hartong, Y. Lei and N. A. Obers, Nonrelativistic Chern-Simons theories and three-dimensional Hoˇ rava-Lifshitz gravity, Phys. Rev. D 94 (2016) 065027 [ 1604.08054]

    2016 arXiv

  79. [87]

    Kasikci, N

    O. Kasikci, N. Ozdemir, M. Ozkan and U. Zorba, Three-dimensional higher-order Schr¨ odinger algebras and Lie algebra expansions , JHEP 04 (2020) 067 [ 2002.03558]

    2020 arXiv

  80. [88]

    Hansen, J

    D. Hansen, J. Hartong and N. A. Obers, Non-Relativistic Gravity and its Coupling to Matter , JHEP 06 (2020) 145 [ 2001.10277]

    2020 arXiv

  81. [89]

    Hansen, J

    D. Hansen, J. Hartong and N. A. Obers, Gravity between Newton and Einstein , Int. J. Mod. Phys. D 28 (2019) 1944010 [ 1904.05706]

    2019 arXiv

  82. [90]

    D. M. Hofman and S. Vitouladitis, Generalised symmetries and state-operator correspondence for nonlocal operators, JHEP 02 (2025) 061 [ 2406.02662]

    2025 arXiv

  83. [91]

    Bagchi and R

    A. Bagchi and R. Gopakumar, Galilean Conformal Algebras and AdS/CFT , JHEP 07 (2009) 037 [0902.1385]

    2009 arXiv

  84. [92]

    Henkel, Local scale invariance and strongly anisotropic equilibrium critical systems , Physical review letters 78 (1997) 1940

    M. Henkel, Local scale invariance and strongly anisotropic equilibrium critical systems , Physical review letters 78 (1997) 1940. – 37 –

    1997

  85. [93]

    Negro, M

    J. Negro, M. Del Olmo and A. Rodrıguez-Marco, Nonrelativistic conformal groups, Journal of Mathematical Physics 38 (1997) 3786

    1997

  86. [94]

    Masterov, Towards ℓ-conformal Galilei algebra via contraction of the conformal group , Nucl

    I. Masterov, Towards ℓ-conformal Galilei algebra via contraction of the conformal group , Nucl. Phys. B 998 (2024) 116395 [ 2309.01588]

    2024 arXiv

  87. [95]

    Duval, G

    C. Duval, G. W. Gibbons and P. A. Horvathy, Conformal Carroll groups and BMS symmetry , Class. Quant. Grav. 31 (2014) 092001 [ 1402.5894]

    2014 arXiv

  88. [96]

    Bagchi, A

    A. Bagchi, A. Mehra and P. Nandi, Field Theories with Conformal Carrollian Symmetry , JHEP 05 (2019) 108 [ 1901.10147]

    2019 arXiv

  89. [97]

    J. B. Gutowski and H. S. Reall, General supersymmetric AdS5 black holes , JHEP 04 (2004) 048 [hep-th/0401129]

    2004 arXiv

  90. [98]

    Grant, P

    L. Grant, P. A. Grassi, S. Kim and S. Minwalla, Comments on 1/16 BPS Quantum States and Classical Configurations, JHEP 05 (2008) 049 [ 0803.4183]

    2008 arXiv

  91. [99]

    S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT , 1810.12067

    arXiv

  92. [100]

    Benini and P

    F. Benini and P. Milan, Black Holes in 4D N =4 Super-Yang-Mills Field Theory , Phys. Rev. X 10 (2020) 021037 [ 1812.09613]

    2020 arXiv

  93. [101]

    Murthy, Growth of the 1 16 -BPS index in 4d N = 4 supersymmetric Yang-Mills theory, Phys

    S. Murthy, Growth of the 1 16 -BPS index in 4d N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 105 (2022) L021903 [ 2005.10843]

    2022 arXiv

  94. [102]

    Goldstein, V

    K. Goldstein, V. Jejjala, Y. Lei, S. van Leuven and W. Li, Residues, modularity, and the Cardy limit of the 4d N = 4 superconformal index , JHEP 04 (2021) 216 [ 2011.06605]

    2021 arXiv

  95. [103]

    Aharony, F

    O. Aharony, F. Benini, O. Mamroud and E. Milan, A gravity interpretation for the Bethe Ansatz expansion of the N = 4 SYM index , Phys. Rev. D 104 (2021) 086026 [ 2104.13932]

    2021 arXiv

  96. [104]

    Chang and Y.-H

    C.-M. Chang and Y.-H. Lin, Words to describe a black hole , JHEP 02 (2023) 109 [2209.06728]

    2023 arXiv

  97. [105]

    Cabo-Bizet, D

    A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS 5 black holes , JHEP 10 (2019) 062 [1810.11442]

    2019 arXiv

  98. [106]

    Gunaydin, A

    M. Gunaydin, A. Neitzke, O. Pavlyk and B. Pioline, Quasi-conformal actions, quaternionic discrete series and twistors: SU (2,1) and G2(2), Commun. Math. Phys. 283 (2008) 169 [0707.1669]

    2008 arXiv

  99. [107]

    C. D. A. Blair, J. Lahnsteiner, N. A. J. Obers and Z. Yan, Unification of Decoupling Limits in String and M Theory , Phys. Rev. Lett. 132 (2024) 161603 [ 2311.10564]

    2024 arXiv

  100. [108]

    Gomis and Z

    J. Gomis and Z. Yan, Worldsheet formalism for decoupling limits in string theory , JHEP 07 (2024) 102 [ 2311.10565]

    2024 arXiv

  101. [109]

    Lambert and J

    N. Lambert and J. Smith, Reciprocal Non-Relativistic Decoupling Limits of String Theory and M-Theory, 2410.17074

    arXiv

  102. [110]

    U-duality and Theories without Gravity

    R. Dijkgraaf, J. de Boer, T. Harmark and N. A. Obers, “ U-duality and Theories without Gravity.”

  103. [111]

    Harmark, J

    T. Harmark, J. Lahnsteiner and N. A. Obers, Gravitational solitons and non-relativistic string theory, 2501.10178. – 38 –

    arXiv

  104. [112]

    S. Choi, S. Kim, E. Lee and J. Park, The shape of non-graviton operators for SU(2) , JHEP 09 (2024) 029 [ 2209.12696]

    2024 arXiv

  105. [113]

    S. Choi, S. Kim, E. Lee, S. Lee and J. Park, Towards quantum black hole microstates , JHEP 11 (2023) 175 [ 2304.10155]

    2023 arXiv

  106. [114]

    J. Choi, S. Choi, S. Kim, J. Lee and S. Lee, Finite N black hole cohomologies , JHEP 12 (2024) 029 [2312.16443]

    2024 arXiv

  107. [115]

    Chang and Y.-H

    C.-M. Chang and Y.-H. Lin, Holographic covering and the fortuity of black holes , 2402.10129

    arXiv

  108. [116]

    Dorey, R

    N. Dorey, R. Mouland and B. Zhao, Black hole entropy from quantum mechanics , JHEP 06 (2023) 166 [ 2207.12477]

    2023 arXiv

  109. [117]

    Dorey and R

    N. Dorey and R. Mouland, Conformal quantum mechanics, holomorphic factorisation, and ultra-spinning black holes , JHEP 02 (2024) 086 [ 2302.14850]

    2024 arXiv

  110. [118]

    Mouland, How to build a black hole out of instantons , JHEP 03 (2024) 002 [ 2311.13636]

    R. Mouland, How to build a black hole out of instantons , JHEP 03 (2024) 002 [ 2311.13636]

    2024 arXiv

  111. [119]

    Maldacena, D

    J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry , JHEP 10 (2008) 072 [ 0807.1100]

    2008 arXiv

  112. [120]

    L. C. Biedenharn, J. Nuyts and N. Straumann, On the unitary representations of su(1, 1) and su(2, 1), Annales de l’institut Henri Poincar´ e. Section A, Physique Th´ eorique3 (1965) 13

    1965

  113. [121]

    Bars and Z.-j

    I. Bars and Z.-j. Teng, The unitary irreducible representations of su (2, 1) , Journal of mathematical physics 31 (1990) 1576

    1990

  114. [122]

    Papageorgiou and B

    G. Papageorgiou and B. J. Schroers, A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions , JHEP 11 (2009) 009 [ 0907.2880]

    2009 arXiv

  115. [123]

    E. A. Bergshoeff and J. Rosseel, Three-Dimensional Extended Bargmann Supergravity, Phys. Rev. Lett. 116 (2016) 251601 [ 1604.08042]

    2016 arXiv

  116. [124]

    Papageorgiou and B

    G. Papageorgiou and B. J. Schroers, Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra, JHEP 11 (2010) 020 [ 1008.0279]

    2010 arXiv

  117. [125]

    Hartong, Y

    J. Hartong, Y. Lei, N. A. Obers and G. Oling, Zooming in on AdS 3/CFT2 near a BPS bound , JHEP 05 (2018) 016 [ 1712.05794]. – 39 –

    2018 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.