Higher symmetries, anomalies, and crossed squares in lattice gauge theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913955366043648 |
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| author | Kapustin, Anton Spodyneiko, Lev |
| author_facet | Kapustin, Anton Spodyneiko, Lev |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher symmetries, anomalies, and crossed squares in lattice gauge theory Kapustin, Anton Spodyneiko, Lev High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra 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. |
| title | Higher symmetries, anomalies, and crossed squares in lattice gauge theory |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2507.16966 |