Cartier integration of infinitesimal 2-braidings via 2-holonomy of the CMKZ 2-connection, I: Hexagonators and the Breen polytope
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909720467472384 |
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| author | Kemp, Cameron James Deverall |
| author_facet | Kemp, Cameron James Deverall |
| contents | This paper follows on from "Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings". Given a symmetric strict infinitesimal 2-braiding on a symmetric strict monoidal cochain 2-category, we construct a candidate hexagonator series as a 2-holonomy with respect to the Cirio-Martins-Knizhnik-Zamolodchikov (CMKZ) fake flat 2-connection over the configuration space of 3 distinguishable particles on the complex line, $Y_3$. The second-order term of the hexagonator series is computed and found to agree with the "infinitesimal hexagonator" from the aforementioned work. Finally, we assume a coherent totally symmetric strict infinitesimal 2-braiding and prove that the Breen polytope axiom is satisfied by translating it into a 2-loop in $Y_3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cartier integration of infinitesimal 2-braidings via 2-holonomy of the CMKZ 2-connection, I: Hexagonators and the Breen polytope Kemp, Cameron James Deverall Quantum Algebra Mathematical Physics Category Theory 17B37, 18N10, 53D55, 32S40 This paper follows on from "Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings". Given a symmetric strict infinitesimal 2-braiding on a symmetric strict monoidal cochain 2-category, we construct a candidate hexagonator series as a 2-holonomy with respect to the Cirio-Martins-Knizhnik-Zamolodchikov (CMKZ) fake flat 2-connection over the configuration space of 3 distinguishable particles on the complex line, $Y_3$. The second-order term of the hexagonator series is computed and found to agree with the "infinitesimal hexagonator" from the aforementioned work. Finally, we assume a coherent totally symmetric strict infinitesimal 2-braiding and prove that the Breen polytope axiom is satisfied by translating it into a 2-loop in $Y_3$. |
| title | Cartier integration of infinitesimal 2-braidings via 2-holonomy of the CMKZ 2-connection, I: Hexagonators and the Breen polytope |
| topic | Quantum Algebra Mathematical Physics Category Theory 17B37, 18N10, 53D55, 32S40 |
| url | https://arxiv.org/abs/2508.01944 |