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Higher symmetries, anomalies, and crossed squares in lattice gauge theory
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We examine higher-form symmetries of quantum lattice gauge theories through the lens of homotopy theory and operator algebras. We show that in the operator-algebraic approach both higher-form symmetries and 't Hooft anomalies arise from considering restrictions of symmetry transformations to spatial regions. The data of these restrictions are naturally packaged into a higher group. For example, for gauge theories in two spatial dimensions, this information is encoded in a crossed square of groups, which is an algebraic model of a 3-group. In general, we propose that higher groups appear in lattice models and QFT as crossed n-cubes of groups via a nonabelian version of the Cech construction.
Forward citations
Cited by 2 Pith papers
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Explicit Pauli stabilizer models are constructed for higher-form Dijkgraaf-Witten TQFTs and new fermionic/anyonic statistics of loop, membrane, and volume excitations are computed on the lattice.
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