String-net models for pivotal bicategories
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909639708246016 |
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| author | Fuchs, Jürgen Schweigert, Christoph Yang, Yang |
| author_facet | Fuchs, Jürgen Schweigert, Christoph Yang, Yang |
| contents | We develop a string-net construction of a modular functor whose algebraic input is a pivotal bicategory; this extends the standard construction based on a spherical fusion category. An essential ingredient in our construction is a graphical calculus for pivotal bicategories, which we express in terms of a category of colored corollas. The globalization of this calculus to oriented surfaces yields the bicategorical string-net spaces as colimits. We show that every rigid separable Frobenius functor between strictly pivotal bicategories induces linear maps between the corresponding bicategorical string-net spaces that are compatible with the mapping class group actions and with sewing. Our results are inspired by and have applications to the description of correlators in two-dimensional conformal field theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01468 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | String-net models for pivotal bicategories Fuchs, Jürgen Schweigert, Christoph Yang, Yang Quantum Algebra High Energy Physics - Theory Mathematical Physics Category Theory We develop a string-net construction of a modular functor whose algebraic input is a pivotal bicategory; this extends the standard construction based on a spherical fusion category. An essential ingredient in our construction is a graphical calculus for pivotal bicategories, which we express in terms of a category of colored corollas. The globalization of this calculus to oriented surfaces yields the bicategorical string-net spaces as colimits. We show that every rigid separable Frobenius functor between strictly pivotal bicategories induces linear maps between the corresponding bicategorical string-net spaces that are compatible with the mapping class group actions and with sewing. Our results are inspired by and have applications to the description of correlators in two-dimensional conformal field theories. |
| title | String-net models for pivotal bicategories |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Category Theory |
| url | https://arxiv.org/abs/2302.01468 |