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
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abstract
For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions, and determine the fusion rule. From a direct analysis of one-form symmetry protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. We give an explicit realization of this duality defect in the free Maxwell theory, both in the continuum and in a modified Villain lattice model. The duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides. We further construct the duality defect in non-abelian gauge theories and the $\mathbb{Z}_N$ lattice gauge theory.
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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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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
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Stringy T-duality on the lattice and the twisted Villain model
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Non-invertible Symmetries in Weyl Fermions, and Applications to Fermion-Boundary Scattering Problem
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Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions
Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.
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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
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Generalized Families of QFTs
Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
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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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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
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Symmetry TFTs from String Theory
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Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation
The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.
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Monodromy Defects for Electric-Magnetic Duality, Hyperbolic Space, and Lines
Monodromy defects in Maxwell theory are analyzed via mapping to hyperbolic space, recovering the defect primary spectrum and showing that Wilson/'t Hooft lines terminate on defects, become decomposable, and follow Chern-Simons topological behavior.
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Self-$G$-ality in 1+1 dimensions
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Universalities of Defects in Quantum Field Theories
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
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ICTP Lectures on (Non-)Invertible Generalized Symmetries
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
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- When Symmetries Twist: Anomaly Inflow on Monodromy Defects
- Half-Spacetime Gauging of 2-Group Symmetry in 3d