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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Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities
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2026 6representative citing papers
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.
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.
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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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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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.
- When Symmetries Twist: Anomaly Inflow on Monodromy Defects