Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909318704529408 |
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| author | Sharapov, Alexey Skvortsov, Evgeny Van Dongen, Richard |
| author_facet | Sharapov, Alexey Skvortsov, Evgeny Van Dongen, Richard |
| contents | Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the first two maps are related to the (Shoikhet-Tsygan-)Kontsevich Formality. As with the known formality theorems, we prove the $A_\infty$-relations via Stokes' theorem by constructing a closed form and a configuration space whose boundary components lead to the $A_\infty$-relations. This gives a new way to formulate higher spin gravities and hints at a construct encompassing the known formality theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16573 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem Sharapov, Alexey Skvortsov, Evgeny Van Dongen, Richard High Energy Physics - Theory Quantum Algebra Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the first two maps are related to the (Shoikhet-Tsygan-)Kontsevich Formality. As with the known formality theorems, we prove the $A_\infty$-relations via Stokes' theorem by constructing a closed form and a configuration space whose boundary components lead to the $A_\infty$-relations. This gives a new way to formulate higher spin gravities and hints at a construct encompassing the known formality theorems. |
| title | Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem |
| topic | High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2312.16573 |