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arXiv · 2312.16573

Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem

Alexey Sharapov·Evgeny Skvortsov·Richard Van Dongen
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Abstract

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.

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Alexey Sharapov, Evgeny Skvortsov, Richard Van Dongen. 2023-12-27. Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem. https://arxiv.org/abs/2312.16573

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