Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem

TL;DR

This paper introduces a novel formulation of chiral higher spin gravity using strong homotopy algebras, where structure maps are expressed as integrals over configuration spaces, linking to formality theorems through Stokes' theorem.

Contribution

It develops a new approach to higher spin gravity by employing configuration space integrals and homotopy algebra structures, connecting to formality theorems via Stokes' theorem.

Findings

Established a new formulation of higher spin gravity using homotopy algebras.

Proved $A_$-relations via Stokes' theorem with configuration space integrals.

Linked the structure maps to Kontsevich formality and noncommutative Poisson structures.

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.