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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Even-length antiferromagnetic ground state of the critical golden chain carries exact Fibonacci cut-charge weights P_tau/P_1=phi^2 and boundary entropy log g=log phi for the duality defect.
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.
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
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.
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.
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.
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).
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
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.
E∞^{1,2}-type LSM anomalies lead to non-invertible symmetry breaking at type-II deconfined quantum critical points in 1D spin chains.
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
For dual massive RG flows, the gapped-phase module is spanned by smeared Ishibashi states and cannot be reduced to the boundary-critical Cardy-state module, even in the simplest tricritical-Ising to Ising flow.
The five-dimensional topological axion electrodynamics is shown to possess a 3-crossed module structure through modified Stueckelberg couplings required for background gauge invariance.
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.
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.
Generalizes spurion analysis to non-invertible near-group fusion algebras, introduces coupling labels, and explains radiative violation of tree-level selection rules.
In Z2 topological order enriched by subsystem symmetries, mobility classes obey multi-channel fusion algebras including Fibonacci rules, tensor products thereof, and lineon period transmutation.
Develops a holographic realization of approximate higher-form symmetries via massive antisymmetric tensor fields and derives dualities between boundary theories from bulk Hodge dualities, including constraints on current-current correlators for self-dual cases.
A modified boost-operator method yields new integrable anyonic chains (including su(2)_k spin-3/2, TY(Z_n), Fib×Fib, Fib×Ising) and a criterion for when Temperley-Lieb algebras appear.
Derives additivity and fusion rules for defect g-functions in integrable 2D QFT, with effective amplitudes for non-topological cases and lowered entropy contribution in Ising non-topological fusion.
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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Entanglement fingerprint of a non-invertible symmetry: exact Fibonacci cut charges on the lattice
Even-length antiferromagnetic ground state of the critical golden chain carries exact Fibonacci cut-charge weights P_tau/P_1=phi^2 and boundary entropy log g=log phi for the duality defect.
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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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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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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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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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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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Non-invertible symmetries in the axiverse, and the imaginary wormholes
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
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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.
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$E_\infty^{1,2}$-type Lieb-Schultz-Mattis anomalies, deconfined quantum critical points, and non-invertible symmetry breaking
E∞^{1,2}-type LSM anomalies lead to non-invertible symmetry breaking at type-II deconfined quantum critical points in 1D spin chains.
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Notes on (-2)-form symmetries
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
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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.
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Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
For dual massive RG flows, the gapped-phase module is spanned by smeared Ishibashi states and cannot be reduced to the boundary-critical Cardy-state module, even in the simplest tricritical-Ising to Ising flow.
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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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Generalized Families of QFTs
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
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The Line, the Strip and the Duality Defect
The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.
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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.
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Spurion Analysis for Non-Invertible Selection Rules from Near-Group Fusions
Generalizes spurion analysis to non-invertible near-group fusion algebras, introduces coupling labels, and explains radiative violation of tree-level selection rules.
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Fusion Rules of Mobility
In Z2 topological order enriched by subsystem symmetries, mobility classes obey multi-channel fusion algebras including Fibonacci rules, tensor products thereof, and lineon period transmutation.
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Approximate higher-form symmetries and dualities of massive p-forms in the holographic bulk
Develops a holographic realization of approximate higher-form symmetries via massive antisymmetric tensor fields and derives dualities between boundary theories from bulk Hodge dualities, including constraints on current-current correlators for self-dual cases.
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Constrained integrability and anyonic chains
A modified boost-operator method yields new integrable anyonic chains (including su(2)_k spin-3/2, TY(Z_n), Fib×Fib, Fib×Ising) and a criterion for when Temperley-Lieb algebras appear.
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Fusion of Integrable Defects and the Defect $g$-Function
Derives additivity and fusion rules for defect g-functions in integrable 2D QFT, with effective amplitudes for non-topological cases and lowered entropy contribution in Ising non-topological fusion.
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Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
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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.
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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.