Modified Villain lattice realizations of flat-gauged interfaces and T-duality defects in the 2D compact boson are constructed at arbitrary radii, yielding non-compact edge modes with continuous spectrum and infinite quantum dimension.
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Generalized Global Symmetries
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A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.
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- abstract A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either complete
- method metriesingeometricengineeringconstructionsofquantumfieldtheoriesviastringtheory, and the study of higher-form symmetries using holographic duality. 2 Introduction to Higher-Form Symmetries The aim of this section is to introducep-form symmetries. These symmetries generalize the usual global symmetries, which in this language are referred to as 0-form symmetries. We will follow the seminal work [4], though this is not to say that this was the first work discussing such ideas. In fact, many of the
- background Somewhat later, a seemingly unrelated-at the time (see the last paragraph in this Section)-development was inspired by the work of Ünsal from 2007 [9, 10]. He showed that objects of fractional topological charge were behind semiclassical confinement and chiral symmetry breaking onR3 ×S 1. The fractionally-charged objects are the so-called "monopole- instantons;" see the review [11] for an extensive list of references. The more recent interest in the subject was driven by the improved understandi
- background While defects are rich subjects of study in their own right, they also serve as powerful tools to understand the quantum field theories in which they are embedded. In particular, we note that certain defects can be continuously deformed without affecting any physical observables. These are topological defects, which generalize the very notion of symmetry in modern physics [1, 2]. This perspective has shed new light on many profound phenomena in quantum field theories, and we will apply it extens
- background 4 The combination U(1)B−L is exactly preserved in the SM, but is expected to be violated by physics beyond the SM (BSM). 5 These are symmetric tensors of the Lorentz group with s≥ 3 indices. By contrast, the stress tensor Tµν is a two-index Lorentz tensor of spin s = 2. 6 A CFT analogue of the CM theorem was proved in [16]. 7 We sometimes call U (0)(g, Σd−1) a symmetry defect. For an exposition of this perspective, see for instance [21] and refer- ences therein. Throughout we use X (p) to indica
- background Verstraete,Anyons and matrix product operator algebras,Annals Phys. 378(2017) 183-233, arXiv:1511.08090 [cond-mat.str-el]. [41] R. Vanhove, M. Bal, D. J. Williamson, N. Bultinck, J. Haegeman, and F. Verstraete,Mapping topological to conformal field theories through strange correlators, Phys. Rev. Lett.121(2018) 177203, arXiv:1801.05959 [quant-ph]. [42] K. Inamura,Topological field theories and symmetry protected topological phases with fusion category symmetries,Journal of High Energy Physics202
- background Alternatively, it is sourced by a localizedG-flux (fractional, in the discrete case). 1 Introduction The space of defects in a quantum system has been the subject of intense recent study: defects arise naturally as impurities in condensed-matter setups, and serve as probes of strongly coupled bulk dy- namics. Topological defects in particular - i.e. symmetries [1] - have led to a wealth of constraints on the long-distance physics, and their classification across dimensions has reached an increas
co-cited works
representative citing papers
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
A derived-geometric definition of p-form connections on infinity-bundles is given via splittings of the Atiyah L-infinity-algebroid, recovering Cech-Deligne cocycles for higher U(1)-bundles.
New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and lattice models.
Constructs a family of non-relativistic limits of 4d MSYM via brane setups that organize into a 3D moduli space with nontrivial topology where PSL(2,Z) dualities act more complexly than in the relativistic theory, establishing Abelian duality by path integral and supporting non-Abelian case via spec
Defines defect skein modules for 3-manifolds with line and point defects and proves they match state spaces of defect Reshetikhin-Turaev TQFT for semisimple data.
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
Introduces the twisted Villain model to realize exact T-duality on the lattice for fibred manifolds, recovering bundle-flux exchange and defining topological defects via half-gauging.
Constructs a family of non-invertible topological defects in n Weyl fermion theories via unfolding of G-symmetric boundary conditions for Dirac fermions, with explicit descriptions for U(1)^n and applications to fermion-boundary scattering.
Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
Derives Schwinger-Dyson equations and Ward identities in NN-FT to study anomalies in QFTs via a conserved parameter-space current, yielding a new perspective on symmetries.
CMB polarization rotation emerges as a Pancharatnam phase localized at dark sector vacuum interfaces, independent of redshift, frequency, and the presence of light axions.
Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.
The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
A supersymmetric SymTFT (SuSymTFT) is constructed as a super-BF theory on (n|m)-dimensional supermanifolds and verified for compact and chiral super-bosons in two dimensions.
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Classification of 2D fermionic systems with Z2 flavor symmetry yields 16 consistent superfusion categories labeled by anomaly invariants (ν_W, ν_Z, ν_WZ).
A general prescription is formulated for spurion analysis of commutative non-invertible fusion algebras in particle physics, unifying prior specific cases and enabling systematic tracking of coupling constants in tree- and loop-level processes without requiring faithful realization or exclusive use.
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
A gauging method from abelian Dijkgraaf-Witten theories yields BF-type Lagrangians for non-abelian cases via local-coefficient cohomologies and homotopy analysis.
Modulated SPT phases in 1D are classified by H²(G, U(1)_s) and obey LSM-type theorems forbidding symmetric short-range entangled ground states.
citing papers explorer
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Lattice Realizations of Flat Gauging and T-duality Defects at Any Radius
Modified Villain lattice realizations of flat-gauged interfaces and T-duality defects in the 2D compact boson are constructed at arbitrary radii, yielding non-compact edge modes with continuous spectrum and infinite quantum dimension.
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Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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Symmetries and Higher-Form Connections in Derived Differential Geometry
A derived-geometric definition of p-form connections on infinity-bundles is given via splittings of the Atiyah L-infinity-algebroid, recovering Cech-Deligne cocycles for higher U(1)-bundles.
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Non-Invertible Anyon Condensation and Level-Rank Dualities
New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
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Non-Invertible Duality Defects in 3+1 Dimensions
Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and lattice models.
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Non-relativistic limits of $\mathcal N=4$ supersymmetric Yang-Mills theory and S-duality
Constructs a family of non-relativistic limits of 4d MSYM via brane setups that organize into a 3D moduli space with nontrivial topology where PSL(2,Z) dualities act more complexly than in the relativistic theory, establishing Abelian duality by path integral and supporting non-Abelian case via spec
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Defects in skein theory and TQFT
Defines defect skein modules for 3-manifolds with line and point defects and proves they match state spaces of defect Reshetikhin-Turaev TQFT for semisimple data.
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Twin Algebras: Condensable Algebras beyond Anyons
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
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Topological lattice gauge theory enriched by non-invertible symmetry
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
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Stringy T-duality on the lattice and the twisted Villain model
Introduces the twisted Villain model to realize exact T-duality on the lattice for fibred manifolds, recovering bundle-flux exchange and defining topological defects via half-gauging.
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Non-invertible Symmetries in Weyl Fermions, and Applications to Fermion-Boundary Scattering Problem
Constructs a family of non-invertible topological defects in n Weyl fermion theories via unfolding of G-symmetric boundary conditions for Dirac fermions, with explicit descriptions for U(1)^n and applications to fermion-boundary scattering.
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Protected operators in non-local defect CFTs from AdS
Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
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Anomalies in Neural Network Field Theory
Derives Schwinger-Dyson equations and Ward identities in NN-FT to study anomalies in QFTs via a conserved parameter-space current, yielding a new perspective on symmetries.
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CMB Birefringence from Vacuum Interfaces
CMB polarization rotation emerges as a Pancharatnam phase localized at dark sector vacuum interfaces, independent of redshift, frequency, and the presence of light axions.
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Sharpened Dynamical Cobordism
Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.
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Symmetry breaking phases and transitions in an Ising fusion category lattice model
The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
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SymTFT in Superspace
A supersymmetric SymTFT (SuSymTFT) is constructed as a super-BF theory on (n|m)-dimensional supermanifolds and verified for compact and chiral super-bosons in two dimensions.
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Generalized Complexity Distances and Non-Invertible Symmetries
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
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Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
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Classification of 2D Fermionic Systems with a $\mathbb Z_2$ Flavor Symmetry
Classification of 2D fermionic systems with Z2 flavor symmetry yields 16 consistent superfusion categories labeled by anomaly invariants (ν_W, ν_Z, ν_WZ).
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A General Prescription for Spurion Analysis of Non-Invertible Selection Rules
A general prescription is formulated for spurion analysis of commutative non-invertible fusion algebras in particle physics, unifying prior specific cases and enabling systematic tracking of coupling constants in tree- and loop-level processes without requiring faithful realization or exclusive use.
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Lattice chiral symmetry from bosons in 3+1d
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
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On Lagrangians of Non-abelian Dijkgraaf-Witten Theories
A gauging method from abelian Dijkgraaf-Witten theories yields BF-type Lagrangians for non-abelian cases via local-coefficient cohomologies and homotopy analysis.
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Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints
Modulated SPT phases in 1D are classified by H²(G, U(1)_s) and obey LSM-type theorems forbidding symmetric short-range entangled ground states.
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On the SymTFTs of Finite Non-Abelian Symmetries
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
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The Line, the Strip and the Duality Defect
Condensation defects in SymTFT descriptions of XY-plaquette and XYZ-cube models realize non-invertible self-duality symmetries at any coupling, with a continuous SO(2) version in the XY-plaquette.
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Non-Abelian and Type-A Conformal Anomalies from Euler Descent
Non-Abelian conformal anomalies are classified via Stora-Zumino descent from the Euler class, placing them on equal footing with perturbative anomalies and enabling WZW terms for anomaly matching.
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Phases of Giant Magnetic Vortex Strings
Giant vortex strings in 3+1D Abelian Higgs models admit essentially exact solutions that fall into sharply distinct phases in the large-n limit, determined by the form of the Higgs potential and governing their binding energies and stability.
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SymTFT construction of gapless exotic-foliated dual models
Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY plaquette and XYZ cube models.
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Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
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Fractonic solids
The authors introduce fractonic solids via a new symmetry that ties fracton mobility to a material, enabling gauge-invariant momentum, boost compatibility, and gravitational coupling.
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Lattice Models for Phases and Transitions with Non-Invertible Symmetries
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
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Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
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Symmetry TFTs from String Theory
Constructs Symmetry TFTs for M-theory compactifications by reducing the topological sector of 11d supergravity on the boundary of X using differential cohomology, with applications to 7d SYM and 5d SCFTs confirmed via IIB 5-brane webs.
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First steps towards gauge-independent vortex identification through machine learning
A neural network trained on 2D SU(2) lattices with inserted thin Z2 vortices, after random gauge transformations, noise, and cooling, can locate center vortices at moderate visibility levels and scales via tiling.
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Revisiting boundary electromagnetic duality and edge modes
In 4D Maxwell theory, standard Neumann/Dirichlet boundary conditions render large gauge transformations and edge mode shifts as gauge redundancies, while modified conditions make them physical symmetries generated by topological surface operators, with new electromagnetic dual boundary conditions co
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Universal Confining Strings: From Compact QED to the Hadron Spectrum
Compact QED in the dyon phase maps to a massive two-form field whose IR fixed-point string theory reproduces a generalized Arvis potential and matches heaviest quarkonium mass ratios to 2.5 percent while raising the Regge intercept above the Nambu-Goto value.
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String probes, simple currents, and the no global symmetries conjecture
Chiral simple current extensions on the worldsheet reproduce and generalize obstructions to gauging center one-form symmetries in 6d and 8d string compactifications while clarifying BPS particle requirements upon circle reduction.
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de Sitter Vacua & pUniverses
The p-Schwinger model on de Sitter space supports p distinct de Sitter-invariant vacua that are Hadamard, and coupling a multi-flavor version to gravity yields a semiclassical de Sitter saddle at large N_f.
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Categorical Symmetries via Operator Algebras
The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra, enabling braiding computations in the 3D SymTFT.
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Candidate Gaugings of Categorical Continuous Symmetry
Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.
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Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.
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Excitability in quantum field theory
For zero-mean Gaussian states in generalized free field theories, one-way local excitability always implies two-way excitability, generalizing the quasiequivalence theorems of Powers, Stormer, van Daele, Araki, and Yamagami.
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Celestial 1-form symmetries
In self-dual Yang-Mills the S-algebra becomes an algebra of 1-form symmetries whose 2-form currents link integrability to the equality of Carrollian corner charges and celestial chiral algebra modes.
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Dynamical Generation of the VY Superpotential in $N=1$ SYM: A Higher-Form Perspective
Higher-form gauge dynamics associated with domain walls produce the VY superpotential semiclassically via Z_N sectors and point-like configurations in N=1 SYM.
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Does hot QCD have a conformal manifold in the chiral limit?
An 't Hooft anomaly at general imaginary baryon chemical potential constrains the QCD chiral transition to three minimal CFT scenarios, with the favored one for N_f >= 3 featuring a conformal manifold of theta_B-dependent universality classes with an exactly marginal operator tied to baryon density.
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3-Crossed Module Structure in the Five-Dimensional Topological Axion Electrodynamics
The five-dimensional topological axion electrodynamics is shown to possess a 3-crossed module structure through modified Stueckelberg couplings required for background gauge invariance.
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Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates
Automorphisms of gauge groups extend to higher or non-invertible symmetries in topological gauge theories and enable transversal non-Clifford gates in 2+1d Z_N qudit Clifford stabilizer models for N greater than or equal to 3.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies
Spatially modulated symmetries arise from gauging ordinary symmetries under generalized LSM anomalies, with explicit lattice models in 2D and 3D plus field-theoretic descriptions in arbitrary dimensions that connect to higher-group structures.