Generalized Global Symmetries

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 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.

49 pages plus appendices. v2: references added

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• Field theories with higher-group symmetry from composite currents
• 't Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Flag manifold sigma models: spin chains and integrable theories
• Probing the dynamics of chiral SU(N) gauge theories via generalized anomalies
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Reflection groups and 3d $\mathcal{N}\ge$ 6 SCFTs
• New Supersymmetric String Theories from Discrete Theta Angles
• An N=1 Lagrangian for an N=3 SCFT
• Surface defects in holographic 5d SCFTs
• Boson-fermion duality with subsystem symmetry
• Cobordism and Deformation Class of the Standard Model
• Landau ordering phase transitions beyond the Landau paradigm
• Fractons and exotic symmetries from branes
• General anomaly matching by Goldstone bosons
• Gauging 1-form center symmetries in simple $SU(N)$ gauge theories
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Non-Simply-Connected Symmetries in 6D SCFTs
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
• Dissipative hydrodynamics with higher-form symmetry
• Fracton Topological Order at Finite Temperature
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Non-Invertible Symmetries in Supergravity
• Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries
• Effective Field Theory of Force-Free Electrodynamics
• Baryons as Quantum Hall Droplets
• Deconfinement on axion domain walls
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Foliated-Exotic Duality in Fractonic BF Theories
• Approximate higher-form symmetries, topological defects, and dynamical phase transitions
• Metastable Vacua in Large-$N$ QCD${}_3$
• Non-invertible symmetries and boundaries in four dimensions
• A study of time reversal symmetry of abelian anyons
• Emergent Dimensions and Braneworlds from Large-N Confinement
• A possible phase for adjoint QCD
• Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Dimensional Reduction of Cobordism and K-theory
• A symmetry principle for gauge theories with fractons
• Looking for structure in the cobordism conjecture
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Characterizing Long-Range Entanglement in a Mixed State Through an Emergent Order on the Entangling Surface
• M5-branes Probing Flux Backgrounds
• Theory of competing Chern-Simons orders and emergent phase transitions
• Comments on compatibility between Conformal symmetry and Continuous higher-form symmetries
• Holographic duals of symmetry broken phases
• The holography of non-invertible self-duality symmetries
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Partially Massless Monopoles and Charges
• String tensions in deformed Yang-Mills theory
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• The gaugino condensate from asymmetric four-torus with twists
• Weakly coupled conformal manifolds in 4d
• Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Fracton magnetohydrodynamics
• Helical magnetic effect and the chiral anomaly
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Toward a 3d Ising model with a weakly-coupled string theory dual
• Modified Villain formulation of abelian Chern-Simons theory
• Emergent entropy production and hydrodynamics in quantum many-body systems
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Green-Schwarz Automorphisms and 6D SCFTs
• Absence of Finite Temperature Phase Transitions in the X-Cube Model and its ${\mathbb{Z}}_p$ Generalization
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• On the stability of topological order in tensor network states
• Discrete gauging and Hasse diagrams
• Chiral 3d SU(3) SQCD and N=2 mirror duality
• Topological violation of global symmetries in quantum gravity
• Emergent gravity from Eguchi-Kawai reduction
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Effective gauge theories of superfluidity with topological order
• Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Fermionic Higher-form Symmetries
• Quantum Statistics and Spacetime Topology: Quantum Surgery Formulas
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Entanglement asymmetry in conformal field theory and holography
• Theory of oblique topological insulators
• Multipole and fracton topological order via gauging foliated SPT phases
• Higher Berry Phase of Fermions and Index Theorem
• Higher-form Symmetries under Weak Measurement
• Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation
• Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Domain Walls and the $CP$ Anomaly in Softly Broken Supersymmetric QCD
• (SPT-)LSM theorems from projective non-invertible symmetries
• Compatible braidings with Hopf links, multi-loop, and Borromean rings in $(3+1)$-dimensional spacetime
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Topological defects
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Non-invertible topological defects in 4-dimensional ${\mathbb{Z}}_2$ pure lattice gauge theory
• DMRG study of the higher-charge Schwinger model and its 't Hooft anomaly
• Bosonization based on Clifford algebras and its gauge theoretic interpretation
• Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon
• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• Gauging non-invertible symmetries on the lattice
• Condensates and anomaly cascade in vector-like theories
• Gauging Lie group symmetry in (2+1)d topological phases
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Anomaly inflow and $p$-form gauge theories
• Self-conjugate QCD
• Dihedral symmetry in $SU(N)$ Yang-Mills theory
• Excitations in strict 2-group higher gauge models of topological phases
• 1-form symmetry versus large N QCD
• When the moduli space is an orbifold: Spontaneous breaking of continuous non-invertible symmetries
• High-temperature domain walls of QCD with imaginary chemical potentials
• High-Quality Axions from Higher-Form Symmetries in Extra Dimensions
• Phase structure of self-dual lattice gauge theories in 4d
• 4-d Chern-Simons Theory: Higher Gauge Symmetry and Holographic Aspects
• Fractons on Graphs and Complexity
• (3+1)D topological orders with only a ${\mathbb{Z}}_2$-charged particle
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Spin Structures and Exact Dualities in Low Dimensions
• A fresh view on string orbifolds
• Proton Stability: From the Standard Model to Beyond Grand Unification
• Finiteness and the Emergence of Dualities
• Unoriented 3d TFTs
• Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries
• Effective Field Theory for Spontaneously Broken Symmetry
• Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Non-Liquid Cellular States
• Symmetry enhancement in RCFT
• Duality viewpoint of criticality
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted $BF$ Theories in Five Dimensions
• Symmetry protected self correcting quantum memory in three space dimensions
• Four-fermion deformations of the massless Schwinger model and confinement
• Topology of $SU(N)$ lattice gauge theories coupled with ${\mathbb{Z}}_N$ $2$-form gauge fields
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Orbifolds from Modular Orbits
• On tensor network representations of the (3+1)d toric code
• Anomalies and phases of strongly-coupled chiral gauge theories: recent developments
• Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Implications of Conformal Symmetry in Quantum Mechanics
• Lattice realization of compact $U(1)$ Chern-Simons theory with exact 1-symmetries
• Vector mesons on the wall
• Linking Entanglement and Discrete Anomaly
• Revisiting relativistic magnetohydrodynamics from quantum electrodynamics
• Is $N=2$ Large?
• Pascal's Triangle Fractal Symmetries
• Non-Invertible Symmetry in Calabi-Yau Conformal Field Theories
• Toric 2-group anomalies via cobordism
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• A Lie based 4-dimensional higher Chern-Simons theory
• Topological confinement of vortices in two-flavor dense QCD
• Instantons to the people: the power of one-form symmetries
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Topological Defects in Floquet Circuits
• Designer non-Abelian fractons from topological layers
• Gauge theory geography: charting a path between semiclassical islands
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• 3-Fermion topological quantum computation
• Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra
• Generalized Yang-Mills Theory and Gravity
• The M-theory origin of global properties of gauge theories
• U(1) spin Chern-Simons theory and Arf invariants in two dimensions
• Higher-form symmetries, anomalous magnetohydrodynamics, and holography
• Entropic order parameters in weakly coupled gauge theories
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Magnetic discrete gauge field in the confining vacua and the supersymmetric index
• Big bang as a topological quantum phase transition
• Gauging the bulk: generalized gauging maps and holographic codes
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• Geometrical tools for embedding fields, submanifolds, and foliations
• Soft theorems for boosts and other time symmetries
• Fractionally Charged Particles at the Energy Frontier: The SM Gauge Group and One-Form Global Symmetry
• On the Global Structure of Deformed Yang-Mills Theory and QCD(adj) on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• On Supersymmetry, Boundary Actions and Brane Charges
• Exploring Confinement in Anti-de Sitter Space
• Systematic Constructions of Fracton Theories
• Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT
• Superfluids, vortices and spinning charged operators in 4d CFT
• Quantum distillation in QCD
• Conformal S-dualities from O-planes
• Bosonization with a background $U(1)$ gauge field
• Dynamical Abelianization and anomalies in chiral gauge theories
• Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Zero sound and higher-form symmetries in compressible holographic phases
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Bootstrapping Lieb-Schultz-Mattis anomalies
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Gapless Topological Order, Gravity, and Black Holes
• Gauge Invariance and Anomalies in Condensed Matter Physics
• Domain walls between 3d phases of Reshetikhin-Turaev TQFTs
• Generalized chiral instabilities, linking numbers, and non-invertible symmetries
• The Fate of Discrete 1-Form Symmetries in 6d
• Measurement-based quantum simulation of Abelian lattice gauge theories
• Witten effect, anomaly inflow, and charge teleportation
• Kac-Moody symmetry in the light front of gauge theories
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• On Topology of the Moduli Space of Gapped Hamiltonians for Topological Phases
• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Categorical-Symmetry Resolved Entanglement in CFT
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Higher-group structure in lattice Abelian gauge theory under instanton-sum modification
• Emergent QCD${}_3$ Quantum Phase Transitions of Fractional Chern Insulators
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Non-invertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry
• Anomalies for anomalous symmetries
• Quantum vortex lattice: Lifshitz duality, topological defects and multipole symmetries
• Comments on Global Symmetries and Anomalies of $5d$ SCFTs
• On Phases of 3d $\mathcal{N}=2$ Chern-Simons-Matter Theories
• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory
• Symmetry Transmutation and Anomaly Matching
• Non-Invertible Peccei-Quinn Symmetry, Natural 2HDM Alignment, and the Visible Axion
• Schwinger model on an interval: analytic results and DMRG
• Piezo-superconductivity: new effects in non-centrosymmetric superconductors
• Strongly coupled QFT dynamics via TQFT coupling
• Gauging U(1) symmetry in (2+1)d topological phases
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
• Polyakov's confinement mechanism for generalized Maxwell theory
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Higgs-confinement continuity and matching of Aharonov-Bohm phases
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Wormhole calculus without averaging from $O(N{)}^{q-1}$ tensor model
• de Sitter Space Decay and Cosmological Constant Relaxation in Unimodular Gravity with Charged Membranes
• Delineating chiral separation effect in two-color dense QCD
• Study of gapped phases of 4d gauge theories using temporal gauging of the ${\mathbb{Z}}_N$ 1-form symmetry
• Holographic models of non-Fermi liquid metals revisited: an effective field theory approach
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Two-dimensional algebra in lattice gauge theory
• $a\times b=c$ in $2+1$D TQFT
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Global anomaly matching in higher-dimensional ${\mathbb{CP}}^{N-1}$ model
• Deep learning lattice gauge theories
• Gapped Boundary Phases of Topological Insulators via Weak Coupling
• Topological mass generation in gapless systems
• Intrinsic mixed state topological order in a stabilizer system under stochastic decoherence: Strong-to-weak spontaneous symmetry breaking from percolation point of view
• Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae
• Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
• Charges in the UV completion of neutral electrodynamics
• Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians
• Flavor Symmetries and Automatic Enhancement in the 6d Supergravity Swampland
• Lectures on 4d N=1 dynamics and related topics
• Category of SET orders
• CT or P Problem and Symmetric Gapped Fermion Solution
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Homological invariants of Pauli stabilizer codes
• Notes on QED Corrections in Weak Decays
• Effective description of non-equilibrium currents in cold magnetized plasma
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Decomposition and the Gross-Taylor string theory
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
• Exotic Invertible Phases with Higher-Group Symmetries
• Dynamical Casimir Effect in a small compact manifold for the Maxwell vacuum
• Two-dimensional Anomaly, Orbifolding, and Boundary States
• Noninvertible operators in one, two, and three dimensions via gauging spatially modulated symmetry
• Geometric Approach to 3D Interfaces at Strong Coupling
• Symmetry fractionalization and duality defects in Maxwell theory
• $3d$ One-form Mixed Anomaly and Entanglement Entropy
• The Phases of Non-supersymmetric Gauge Theories: the $SO(N_c)$ Case Study
• Duality and higher Buscher rules in p-form gauge theory and linearized gravity
• Additivity, Haag duality, and non-invertible symmetries
• Topological aspects of brane fields: solitons and higher-form symmetries
• Renormalization of Ising cage-net model and generalized foliation
• Twisted Partition Functions as Order Parameters
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• On Exotic Consistent Anomalies in (1+1)$d$: A Ghost Story
• Flux Quantization on Phase Space
• On Nieh-Yan Transport
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• The fate of non-supersymmetric Gross-Neveu-Yukawa fixed point in two dimensions
• Ramond-Ramond couplings of D-branes
• Extended Functorial Field Theories and Anomalies in Quantum Field Theories
• Higher Gauge Theory
• Higher Gauge Theory and Integrability
• A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Duality Defect of the Monster CFT
• Spontaneous symmetry breaking in pure 2D Yang-Mills theory
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• LSM and CPT
• Pole-skipping of Holographic Correlators: Aspects of Gauge Symmetry and Generalizations
• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Phase structure of linear quiver gauge theories from anomaly matching
• 't Hooft surface in lattice gauge theory
• Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction
• Excitations of Ising Strings on a Lattice
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Quantum Groups as Global Symmetries
• Solvable Lattice Hamiltonians with Fractional Hall Conductivity
• Simulating Quantum Mechanics with a $\theta$-term and an 't Hooft Anomaly on a Synthetic Dimension
• Interplay between lattice gauge theory and subsystem codes
• Anomalous Continuous Translations
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Gauge interactions and topological phases of matter
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• Anomaly Inflow and Holography
• Rainbow Nambu-Goldstone modes under a shear flow
• Matching higher symmetries across Intriligator-Seiberg duality
• Natural inflation, strong dynamics, and the role of generalized anomalies
• Analytic solutions for the linearized first-order magnetohydrodynamics and implications for causality and stability
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Bipartite Fluctuations of Critical Fermi Surfaces
• Towards absolutely stable ergodicity breaking in two and three dimensions
• Domain Walls in 4d N=1 Supersymmetric Yang-Mills
• Quantum computation by teleportation and symmetry
• Dynamical Edge Modes in $p$-form Gauge Theories
• Symmetry Operators and Gravity
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Monopole Breaking of Chern-Weil Symmetries
• Musings on the Current Status of HEP
• Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory
• Fractionalized holes in one-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to fermion matter -- deconfined dynamics and emergent integrability
• Quantum field theories of extended objects
• Confinement on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and Double-String Collapse
• Topologically ordered time crystals
• Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups
• Spin Structures and AdS${}_4$ Holography
• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Consistency of $\chi$SB in chiral Yang-Mills theory with adiabatic continuity
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Unstable Nambu-Goldstone modes
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Minimal Models RG flows: non-invertible symmetries & non-perturbative description
• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations
• Gravitational higher-form symmetries and the origin of hidden symmetries in Kaluza-Klein compactifications
• Chiral spin liquid in a ${\mathbb{Z}}_3$ Kitaev model
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Self-$G$-ality in 1+1 dimensions
• Impossible Symmetries and Conformal Gravity
• Robust Hilbert space fragmentation in group-valued loop models
• Duality, generalized global symmetries and jet space isometries
• Self-correction from higher-form symmetry protection on a boundary
• Anyon Condensation in Virasoro TQFT: Wormhole Factorization
• Classes of topological qubits from low-dimensional quantum spin systems
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• Holographic duals of the $\mathcal{N}=1$* gauge theory
• Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries
• Quivers, Lattice Gauge Theories and Fractons
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Generalized symmetries of topological field theories
• Higher-form symmetries and $d-wave$ superconductors from doped Mott insulators
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• Topological terms and anomaly matching in effective field theories on ${\mathbb{R}}^3\times S^1$: I. Abelian symmetries and intermediate scales
• Disconnected gauge groups in the infrared
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Dynamical generalization of Yetter's model based on a crossed module of discrete groups
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• ABJ anomaly as a U(1) symmetry and Noether's theorem
• Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory
• Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover
• Isolated zero mode in a quantum computer from a duality twist
• A Multicritical Point with Infinite Fractal Symmetries
• Non-invertible symmetries in finite-group gauge theory
• Operator lifetime and the force-free electrodynamic limit of magnetised holographic plasma
• Edge Theories for Anyon Condensation Phase Transitions
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Duality defect in a deformed transverse-field Ising model
• The Ultraviolet Structure of Quantum Field Theories. Part 3: Gauge Theories
• Compactifying 5d superconformal field theories to 3d
• Disturbing news about the $d=2+\epsilon$ expansion
• Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
• C-P-T Fractionalization
• Ward Identity and Basis Tensor Gauge Theory at One Loop
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Topological defects as lagrangian correspondences
• Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Massless chiral fields in six dimensions
• Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
• Effective field theories of dissipative fluids with one-form symmetries
• WZW terms without anomalies: generalised symmetries in chiral Lagrangians
• Anyon condensation in mixed-state topological order
• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• Higgs Phases and Boundary Criticality
• Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics
• Higher-group global symmetry and the bosonic M5 brane
• 5d SCFTs and their non-supersymmetric cousins
• Note on lattice description of generalized symmetries in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Non-Invertible Gauss Law and Axions
• Non-Invertible $SO(2)$ Symmetry of 4d Maxwell from Continuous Gaugings
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Shear and bulk viscosity for a pure glue theory using an effective matrix model
• von Neumann Subfactors and Non-invertible Symmetries
• Wilson loops in the Hamiltonian formalism
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• (-1)-Form Symmetries and Anomaly Shifting from SymTFT
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• 1-form Symmetries of 4d N=2 Class S Theories
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• Probing Defects with Quantum Simulator Snapshots
• Surface Operators in Superspace
• Generalized Landau Paradigm for quantum phases and phase transitions
• Dynamics of a lattice 2-group gauge theory model
• Higher-form symmetry breaking and holographic flavour
• On the Gauge Group Topology of 8d CHL Vacua
• Extended Gauge Theory Deformations From~Flux~Backgrounds
• Notes on $\mathcal{N}=1$ QCD${}_3$ with baryon superpotential
• Gauge-independent transition separating confinement and Higgs phases in lattice SU(2) gauge theory with a scalar field in the fundamental representation
• OPE of the stress tensors and surface operators
• Systematic construction of stabilizer codes via gauging abelian boundary symmetries
• B-brane transport in anomalous (2,2) models and localization
• Multivalued fields and monopole operators
• Smooth generalized symmetries of quantum field theories
• Pairwise Helicity in Higher Dimensions
• CFTs on curved spaces
• Emergent Supersymmetry on the Edges
• Fractonic superfluids. III. Hybridizing higher moments
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Domain walls in super Yang-Mills: worldvolume TQFTs and deconfinement from semiclassics on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• Vacuum Structures Revisited
• Deconfined Quantum Critical Point with Non-locality
• Non-Abelian Self-Correcting Quantum Memory and Transversal Non-Clifford Gate beyond the $n^{1/3}$ Distance Barrier
• Disentangling anomaly-free symmetries of quantum spin chains
• Negative string tension of higher-charge Schwinger model via digital quantum simulation
• From $\mathcal{N}=4$ Super-Yang-Mills on ${\mathbb{RP}}^4$ to bosonic Yang-Mills on ${\mathbb{RP}}^2$
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Covariant field theory of 3D massive fractons
• Chern-Simons theory, decomposition, and the A model
• Ordering the topological order in the fractional quantum Hall effect
• Abelian duality in topological field theory
• Weak symmetry breaking and topological order in a 3D compressible quantum liquid
• Resistive relativistic magnetohydrodynamics without Amperes Law
• Secondary products in supersymmetric field theory
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Two types of domain walls in $\mathcal{N}=1$ super-QCD: how they are classified and counted
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Interface Junctions in QCD${}_4$
• Generalized symmetry constraints on deformed 4d (S)CFTs
• Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1+1$d conformal field theories
• Tensor supercurrent in QCD
• Searching for Gravity Without a Metric
• First-order CP phase transition in two-flavor QCD at $\theta =\pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• $N$-ality symmetry and SPT phases in (1+1)d
• From gauging to duality in one-dimensional quantum lattice models
• Exploring two dimensional ${\mathbb{Z}}_2$ invariant phases with time reversal symmetry and their transitions with topological operations
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• Swampland conjectures for type IIB orientifolds with closed-string U(1)s
• New Crosscap States
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Anomalies of global symmetries on the lattice
• A landscape of 4d N=1 SCFTs with a=c
• On the classification of duality defects in $c=2$ compact boson CFTs with a discrete group orbifold
• A non-semisimple non-invertible symmetry
• On the relation between fractional charge and statistics
• Flux Backgrounds and Exceptional Generalised Geometry
• Generalized symmetries as homotopy Lie algebras
• Perturbative Unitarity Calls for An Action
• Reconstructing the boundary of AdS from an infrared defect
• Generalized relativistic second order magnetohydrodynamics: A correlation function approach using Zubarev's nonequilibrium statistical operator
• Les Houches Lecture Notes on Tensor Networks
• Intertwined order of generalized global symmetries
• A stabilizer code model with non-invertible symmetries: Strange fractons, confinement, and non-commutative and non-Abelian fusion rules
• Deconfined quantum criticality in Ising gauge theory entangled with single-component fermions
• Global shift symmetry on an ADM hypersurface: Toward emergent gravity
• Photons without vector fields
• Entropic order parameters and topological holography
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization
• Mirror symmetry and the flavor vortex operator in two dimensions
• Entropic Order Parameters for Categorical Symmetries in 2D-CFT
• Threefold Way for Typical Entanglement
• Higher categorical groups and the classification of topological defects and textures
• Abelian Topological Order on Lattice Enriched with Electromagnetic Background
• Proliferation transitions from a topological phase in $2+1$ dimensions
• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles
• Anomaly-induced edge currents in hydrodynamics with parity anomaly
• The Luttinger Count is the Homotopy not the Physical Charge: Generalized Anomalies Characterize Non-Fermi Liquids
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Universal Deformations
• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory
• Non-Abelian basis tensor gauge theory
• Center Symmetry Breaking in Calabi--Yau Compactifications
• SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories
• Covariant Fracton Electrodynamics in Six Dimensions
• Mass Without Mass from a Berry--Shifted SU(3) Holonomy Rotor
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• Lorentz Invariance of Basis Tensor Gauge Theory
• Emergent fracton strings from covariant bi-form gauge field theory
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Superselection Rules, Bosonization Duality in 1+1 Dimensions and Momentum-Space Entanglement
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations
• Web of dualities on non-orientable surfaces
• Topology of Calorons Re-examined
• An effective theory for higher-dimensional black holes and applications to metastable antibranes
• Effective field theory for dissipative photons from higher-form symmetries
• Non-invertible translation from Lieb-Schultz-Mattis anomaly
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
• Obstruction to Ergodicity from Locality and $U(1)$ Higher Symmetries on the Lattice
• Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
• Entanglement Spectrum Resolved by Loop Symmetries
• Higher-form entanglement asymmetry and topological order
• Emergent structures in open EFTs
• Defects in Wigner crystals: fracton-elasticity duality and vacancy proliferation
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains
• Boundary electromagnetic duality from homological edge modes
• A Subsystem Ginzburg-Landau and SPT Orders Co-existing on a Graph
• Higher-form anomalies and state-operator correspondence beyond conformal invariance
• Generalized symmetry enriched criticality in (3+1)d
• Non-Semisimple TQFT's and BPS $q$-Series
• Schur Connections: Chord Counting, Line Operators, and Indices
• The Phases of Chaos
• Symmetry TFTs from String Theory
• Loops in 4+1d Topological Phases
• Current Groups and the Hamiltonian Anomaly
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory
• Factorization and global symmetries in holography
• Aspects of 4d supersymmetric dynamics and geometry
• Global variants of $\mathcal{N}=1^{\ast }$ theories and Calogero-Moser systems
• On the perturbative aspects of deformed Yang-Mills theory
• Decomposition in 2d non-invertible gaugings
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models
• Generalized symmetries and Noether's theorem in QFT
• Lattice defect networks in 2d Yang-Mills
• Instances of Higher Geometry in Field Theory
• Five dimensional $SU(5)\times U(1{)}_{\mathrm{PQ}}$ grand unification
• Hommage a Nambu
• Some Lower Dimensional Quantum Field Theories Reduced from Chern-Simons Gauge Theories
• A concrete construction of a topological operator in factorization algebras