Alterfold Theory and Topological Modular Invariance
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912159784501248 |
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| author | Liu, Zhengwei Ming, Shuang Wang, Yilong Wu, Jinsong |
| author_facet | Liu, Zhengwei Ming, Shuang Wang, Yilong Wu, Jinsong |
| contents | We propose a topological paradigm in alterfold topological quantum field theory to explore various concepts, including modular invariants, $α$-induction and connections in Morita contexts within a modular fusion category of non-zero global dimension over an arbitrary field. Using our topological perspective, we provide streamlined quick proofs and broad generalizations of a wide range of results. These include all theoretical findings by Böckenhauer, Evans, and Kawahigashi on $α$-induction. Additionally, we introduce the concept of double $α$-induction for pairs of Morita contexts and define its higher-genus $Z$-transformation, which remains invariant under the action of the mapping class group. Finally, we establish a novel integral identity for modular invariance across multiple Morita contexts, unifying several known identities as special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alterfold Theory and Topological Modular Invariance Liu, Zhengwei Ming, Shuang Wang, Yilong Wu, Jinsong Quantum Algebra Mathematical Physics Geometric Topology Operator Algebras We propose a topological paradigm in alterfold topological quantum field theory to explore various concepts, including modular invariants, $α$-induction and connections in Morita contexts within a modular fusion category of non-zero global dimension over an arbitrary field. Using our topological perspective, we provide streamlined quick proofs and broad generalizations of a wide range of results. These include all theoretical findings by Böckenhauer, Evans, and Kawahigashi on $α$-induction. Additionally, we introduce the concept of double $α$-induction for pairs of Morita contexts and define its higher-genus $Z$-transformation, which remains invariant under the action of the mapping class group. Finally, we establish a novel integral identity for modular invariance across multiple Morita contexts, unifying several known identities as special cases. |
| title | Alterfold Theory and Topological Modular Invariance |
| topic | Quantum Algebra Mathematical Physics Geometric Topology Operator Algebras |
| url | https://arxiv.org/abs/2412.12702 |