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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Lieb-Schultz-Mattis, Lut- tinger, and ’t Hooft - anomaly matching in lat- tice systems,
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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.
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.
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
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 noncompact Lie group symmetry generated by U(1) fermion number and Majorana translations enforces Fermi surfaces that generically have at least two noncontractible components in d-dimensional Bravais lattices.
Conjecture of an exact formula for 3-point functions of ℓ-leg and diagonal fields in critical loop models, supported by transfer-matrix numerics on cylinders that agree in most cases.
E∞^{1,2}-type LSM anomalies lead to non-invertible symmetry breaking at type-II deconfined quantum critical points in 1D spin chains.
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.
Inelastic neutron scattering on CeCoIn5 shows spin excitations consistent with fractionalized spinons coexisting with d-wave superconductivity near a quantum critical point.
Staggered fermions in 2+1d show modulo 8 parity/time-reversal anomalies that match between lattice and continuum when placed on tori and Klein bottles via a nontrivial symmetry map.
Authors introduce an observable measuring non-locality properties of symmetry operators that encodes fusion algebra information for a class of examples in QFT.
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
A dissertation synthesizing universal aspects of defect dynamics in QFT through symmetry principles across defect RG flows, effective strings, and quantum gas impurities.
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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
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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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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A Twist on Scattering from Defect Anomalies
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
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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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Symmetry-Enforced Fermi Surfaces
A noncompact Lie group symmetry generated by U(1) fermion number and Majorana translations enforces Fermi surfaces that generically have at least two noncontractible components in d-dimensional Bravais lattices.
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Three-point functions in critical loop models
Conjecture of an exact formula for 3-point functions of ℓ-leg and diagonal fields in critical loop models, supported by transfer-matrix numerics on cylinders that agree in most cases.
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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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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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Superconductivity and fractionalized magnetic excitations in CeCoIn5
Inelastic neutron scattering on CeCoIn5 shows spin excitations consistent with fractionalized spinons coexisting with d-wave superconductivity near a quantum critical point.
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Tori, Klein Bottles, and Modulo 8 Parity/Time-reversal Anomalies of 2+1d Staggered Fermions
Staggered fermions in 2+1d show modulo 8 parity/time-reversal anomalies that match between lattice and continuum when placed on tori and Klein bottles via a nontrivial symmetry map.
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Global symmetries: locality, unitarity, and regularity
Authors introduce an observable measuring non-locality properties of symmetry operators that encodes fusion algebra information for a class of examples in QFT.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
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Universalities of Defects in Quantum Field Theories
A dissertation synthesizing universal aspects of defect dynamics in QFT through symmetry principles across defect RG flows, effective strings, and quantum gas impurities.
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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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