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.
hub Canonical reference
Exploring 2-Group Global Symmetries
Canonical reference. 100% of citing Pith papers cite this work as background.
22
Pith papers citing it
Background
100% of classified citations
abstract
We analyze four-dimensional quantum field theories with continuous 2-group global symmetries. At the level of their charges such symmetries are identical to a product of continuous flavor or spacetime symmetries with a 1-form global symmetry $U(1)^{(1)}_B$, which arises from a conserved 2-form current $J_B^{(2)}$. Rather, 2-group symmetries are characterized by deformed current algebras, with quantized structure constants, which allow two flavor currents or stress tensors to fuse into $J_B^{(2)}$. This leads to unconventional Ward identities, which constrain the allowed patterns of spontaneous 2-group symmetry breaking and other aspects of the renormalization group flow. If $J_B^{(2)}$ is coupled to a 2-form background gauge field $B^{(2)}$, the 2-group current algebra modifies the behavior of $B^{(2)}$ under background gauge transformations. Its transformation rule takes the same form as in the Green-Schwarz mechanism, but only involves the background gauge or gravity fields that couple to the other 2-group currents. This makes it possible to partially cancel reducible 't Hooft anomalies using Green-Schwarz counterterms for the 2-group background gauge fields. The parts that cannot be cancelled are reinterpreted as mixed, global anomalies involving $U(1)_B^{(1)}$ and receive contributions from topological, as well as massless, degrees of freedom. Theories with 2-group symmetry are constructed by gauging an abelian flavor symmetry with suitable mixed 't Hooft anomalies, which leads to many simple and explicit examples. Some of them have dynamical string excitations that carry $U(1)_B^{(1)}$ charge, and 2-group symmetry determines certain 't Hooft anomalies on the world sheets of these strings. Finally, we point out that holographic theories with 2-group global symmetries have a bulk description in terms of dynamical gauge fields that participate in a conventional Green-Schwarz mechanism.
hub tools
citation-role summary
background 11
citation-polarity summary
roles
background 11polarities
background 11representative citing papers
A concrete lattice model realizing a type-IV mixed anomaly yields emergent higher-categorical symmetries upon gauging, and the same framework applied to Lieb-Schultz-Mattis systems produces modulated symmetries whose realization is intrinsically defect-dependent.
Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
Constructs non-invertible duality defects in (2+1)d QFTs from half-spacetime gauging of 2-group symmetries and derives explicit fusion rules with examples in U(1)^3 gauge theories.
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.
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.
Establishes a one-to-one correspondence between states and p-dimensional defects in higher-form Maxwell theories via an extended Kac-Moody algebra generated by conserved charges from mixed anomalies, mapping dressed Wilson-'t Hooft defects to squeezed energy eigenstates.
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
Defects for discrete symmetries encoded in bordism groups Ω^ξ_2(BG) and H_2(BG;Z) are described as brane networks rather than isolated objects, extending the Cobordism Conjecture and demonstrated in 4d supergravity from string/M-theory.
The five-dimensional topological axion electrodynamics is shown to possess a 3-crossed module structure through modified Stueckelberg couplings required for background gauge invariance.
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.
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.
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.
Constructs Čech-de Rham bicomplex from gerbe data for BV-BRST complex and anomaly descent of U(1) 1-form symmetries in Maxwell theory.
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, and holographic Romans mass setups.
A quantum mechanical framework is given for Hilbert and defect spaces of line operators in BF+kCS TQFT, with line operator action realized by convolution kernels and matches to Verlinde and semiclassical Hopf-link data.
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
citing papers explorer
-
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.
-
Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems
A concrete lattice model realizing a type-IV mixed anomaly yields emergent higher-categorical symmetries upon gauging, and the same framework applied to Lieb-Schultz-Mattis systems produces modulated symmetries whose realization is intrinsically defect-dependent.
-
Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions
Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
-
Half-Spacetime Gauging of 2-Group Symmetry in 3d
Constructs non-invertible duality defects in (2+1)d QFTs from half-spacetime gauging of 2-group symmetries and derives explicit fusion rules with examples in U(1)^3 gauge theories.
-
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.
-
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.
-
The state/defect correspondence
Establishes a one-to-one correspondence between states and p-dimensional defects in higher-form Maxwell theories via an extended Kac-Moody algebra generated by conserved charges from mixed anomalies, mapping dressed Wilson-'t Hooft defects to squeezed energy eigenstates.
-
Quiver Approach to Symmetry Theories
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
-
A missing link: Brane networks and the Cobordism Conjecture
Defects for discrete symmetries encoded in bordism groups Ω^ξ_2(BG) and H_2(BG;Z) are described as brane networks rather than isolated objects, extending the Cobordism Conjecture and demonstrated in 4d supergravity from string/M-theory.
-
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.
-
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.
-
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.
-
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.
-
On Quantum Aspects of 1-Form Symmetries I: BV-BRST Cohomology and Anomaly Polynomials
Constructs Čech-de Rham bicomplex from gerbe data for BV-BRST complex and anomaly descent of U(1) 1-form symmetries in Maxwell theory.
-
Notes on (-2)-form symmetries
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, and holographic Romans mass setups.
-
Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries
A quantum mechanical framework is given for Hilbert and defect spaces of line operators in BF+kCS TQFT, with line operator action realized by convolution kernels and matches to Verlinde and semiclassical Hopf-link data.
-
Topological symmetry in quantum field theory
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
-
What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
-
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
-
Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.