The Hermitian axiom on two-dimensional topological quantum field theories
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917902614003712 |
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| author | Zhu, Honglin |
| author_facet | Zhu, Honglin |
| contents | In this paper, we examine Atiyah's Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D TQFTs and Frobenius algebras, we find the algebraic objects corresponding to Hermitian and unitary TQFTs respectively and prove structure theorems about them. We then clarify a few older results on unitary TQFTs using our structure theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_07193 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Hermitian axiom on two-dimensional topological quantum field theories Zhu, Honglin Algebraic Topology Mathematical Physics 57K16 In this paper, we examine Atiyah's Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D TQFTs and Frobenius algebras, we find the algebraic objects corresponding to Hermitian and unitary TQFTs respectively and prove structure theorems about them. We then clarify a few older results on unitary TQFTs using our structure theorems. |
| title | The Hermitian axiom on two-dimensional topological quantum field theories |
| topic | Algebraic Topology Mathematical Physics 57K16 |
| url | https://arxiv.org/abs/2206.07193 |