1. Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem
- Author
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Sharapov, Alexey, Skvortsov, Evgeny, and Van Dongen, Richard
- Subjects
High Energy Physics - Theory ,Mathematics - Quantum Algebra - 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., Comment: many figures, too many pages, published version
- Published
- 2023