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
7 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.
Abelian mixed-state anomalies are fixed solely by an algebraic relation between a symmetry and its flux-insertion operator, producing universal symmetry-charge flow across charge sectors.
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
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.
Ensemble averaging in holography is reframed as averaging over topological completions of a relative theory via SymTFT boundary conditions, reproducing known moments in Marolf-Maxfield and Narain models.
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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Anomaly and symmetry-charge flow in mixed states
Abelian mixed-state anomalies are fixed solely by an algebraic relation between a symmetry and its flux-insertion operator, producing universal symmetry-charge flow across charge sectors.
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Notes on (-2)-form symmetries
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
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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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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in holography is reframed as averaging over topological completions of a relative theory via SymTFT boundary conditions, reproducing known moments in Marolf-Maxfield and Narain models.
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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.