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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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.
Lattice CPT symmetry upgrades the Onsager chiral symmetry anomaly from order two to infinite order, better matching the continuum chiral anomaly, with discussion of associated 2+1d SPT phases.
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.
Exotic theta terms in 2+1d fractonic φ-theory induce generalized Witten effects, with vortex operators gaining momentum subsystem charge (quadrupolar for the foliated case).
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 lattice discretization of constant modes in 2+1D Maxwell-Chern-Simons theory on a torus maps to a generalized Harper-Hofstadter model, reproducing continuum topological degeneracy under specific commensurability conditions with truncation convergence analyzed.
Quantization of axions on dS_D yields Hilbert space H = L^2(S^1) ⊗ F with zero-mode U(1) charge, producing non-dS-invariant charged sectors and Hadamard Wightman functions that become asymptotically invariant.
Proposes a bosonized lattice construction of anomaly-free 2D non-Abelian chiral gauge theories in which left and right bulk contributions cancel at finite spacing when quadratic indices match.
Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.
Field theories with ℤ_N p-form symmetry generically admit a Coulomb phase where the infrared theory is Abelian p-form electrodynamics, illustrated via continuum and lattice examples.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
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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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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Infinite-Order Lattice Chiral Anomalies and CPT
Lattice CPT symmetry upgrades the Onsager chiral symmetry anomaly from order two to infinite order, better matching the continuum chiral anomaly, with discussion of associated 2+1d SPT phases.
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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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Exotic theta terms in 2+1d fractonic field theory
Exotic theta terms in 2+1d fractonic φ-theory induce generalized Witten effects, with vortex operators gaining momentum subsystem charge (quadrupolar for the foliated case).
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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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Toward Hamiltonian simulations of Maxwell-Chern-Simons theory: constant modes and gauge field truncation
A lattice discretization of constant modes in 2+1D Maxwell-Chern-Simons theory on a torus maps to a generalized Harper-Hofstadter model, reproducing continuum topological degeneracy under specific commensurability conditions with truncation convergence analyzed.
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Axions on de Sitter space
Quantization of axions on dS_D yields Hilbert space H = L^2(S^1) ⊗ F with zero-mode U(1) charge, producing non-dS-invariant charged sectors and Hadamard Wightman functions that become asymptotically invariant.
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Lattice chiral non-Abelian gauge symmetry via bosonization
Proposes a bosonized lattice construction of anomaly-free 2D non-Abelian chiral gauge theories in which left and right bulk contributions cancel at finite spacing when quadratic indices match.
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Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation
Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.
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When Symmetries Twist: Anomaly Inflow on Monodromy Defects
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.
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Discrete $p$-Form Symmetry and Higher Coulomb Phases
Field theories with ℤ_N p-form symmetry generically admit a Coulomb phase where the infrared theory is Abelian p-form electrodynamics, illustrated via continuum and lattice examples.
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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.