The Fusion Categorical Diagonal
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929342211162112 |
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| author | Robbins, Daniel Vandermeulen, Thomas |
| author_facet | Robbins, Daniel Vandermeulen, Thomas |
| contents | We define a Frobenius algebra over fusion categories of the form Rep$(G)\boxtimes$Rep$(G)$ which generalizes the diagonal subgroup of $G\times G$. This allows us to extend field theoretical constructions which depend on the existence of a diagonal subgroup to non-invertible symmetries. We give explicit calculations for theories with Rep$(S_3)\boxtimes$Rep$(S_3)$ symmetry, applying the results to gauging topological quantum field theories which carry this non-invertible symmetry. Along the way, we also discuss how Morita equivalence is implemented for algebras in symmetry categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Fusion Categorical Diagonal Robbins, Daniel Vandermeulen, Thomas High Energy Physics - Theory Strongly Correlated Electrons Quantum Algebra We define a Frobenius algebra over fusion categories of the form Rep$(G)\boxtimes$Rep$(G)$ which generalizes the diagonal subgroup of $G\times G$. This allows us to extend field theoretical constructions which depend on the existence of a diagonal subgroup to non-invertible symmetries. We give explicit calculations for theories with Rep$(S_3)\boxtimes$Rep$(S_3)$ symmetry, applying the results to gauging topological quantum field theories which carry this non-invertible symmetry. Along the way, we also discuss how Morita equivalence is implemented for algebras in symmetry categories. |
| title | The Fusion Categorical Diagonal |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Algebra |
| url | https://arxiv.org/abs/2405.08058 |