A concrete lattice model realizing a type-IV mixed anomaly yields emergent higher-categorical symmetries upon gauging, and the same framework applied to Lieb-Schultz-Mattis systems produces modulated symmetries whose realization is intrinsically defect-dependent.
Topological interactions in broken gauge theories
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This thesis deals with planar gauge theories in which some gauge group G is spontaneously broken to a finite subgroup H. The spectrum consists of magnetic vortices, global H charges and dyonic combinations exhibiting topological Aharonov-Bohm interactions. Among other things, we review the Hopf algebra D(H) related to this residual discrete H gauge theory, which provides an unified description of the spin, braid and fusion properties of the aforementioned particles. The implications of adding a Chern-Simons (CS) term to these models are also addressed. We recall that the CS actions for a compact gauge group G are classified by the cohomology group H^4(BG,Z). For finite groups H this classification boils down to the cohomology group H^3(H,U(1)). Thus the different CS actions for a finite group H are given by the inequivalent 3-cocycles of H. It is argued that adding a CS action for the broken gauge group G leads to additional topological interactions for the vortices governed by a 3-cocycle for the residual finite gauge group H determined by a natural homomorphism from H^4(BG,Z) to H^3(H,U(1)). Accordingly, the related Hopf algebra D(H) is deformed into a quasi-Hopf algebra. These general considerations are illustrated by CS theories in which the direct product of some U(1) gauge groups is broken to a finite subgroup H. It turns out that not all conceivable 3-cocycles for finite abelian gauge groups H can be obtained in this way. Those that are not reached are the most interesting. A Z_2 x Z_2 x Z_2 CS theory given by such a 3-cocycle, for instance, is dual to an ordinary gauge theory with nonabelian gauge group the dihedral group of order eight. Finally, the CS theories with nonabelian finite gauge group a dihedral or double dihedral group are also discussed in full detail.
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Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov measure in the Narain case.
The chiral anomaly is extended to mixed states via symmetry-charge flow derived algebraically from symmetry and flux-insertion operators, restoring universality for Abelian symmetries in fermionic and bosonic systems.
Algorithms construct stabilizer models for boundaries and 0D defects in composite-dimensional twisted quantum double codes, with examples like Z4 double coupled to double semion phase and threshold comparisons to surface codes.
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.
citing papers explorer
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Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems
A concrete lattice model realizing a type-IV mixed anomaly yields emergent higher-categorical symmetries upon gauging, and the same framework applied to Lieb-Schultz-Mattis systems produces modulated symmetries whose realization is intrinsically defect-dependent.
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On the SymTFTs of Finite Non-Abelian Symmetries
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov measure in the Narain case.
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Anomaly and symmetry-charge flow in mixed states
The chiral anomaly is extended to mixed states via symmetry-charge flow derived algebraically from symmetry and flux-insertion operators, restoring universality for Abelian symmetries in fermionic and bosonic systems.
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Composite-Dimensional Topological Codes with Boundaries and Defects
Algorithms construct stabilizer models for boundaries and 0D defects in composite-dimensional twisted quantum double codes, with examples like Z4 double coupled to double semion phase and threshold comparisons to surface codes.
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Magic and Non-Clifford Gates in Topological Quantum Field Theory
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.