Chiral Higher Spin Gravity and Convex Geometry

TL;DR

This paper constructs an $A_$-algebra for Chiral Higher Spin Gravity, revealing its algebraic structure and connections to convex geometry, with implications for 3d bosonization duality and vector models.

Contribution

It explicitly constructs an $A_$-algebra of pre-Calabi-Yau type for the theory's interactions, linking algebraic structures to convex geometric integrals.

Findings

Constructed an $A_$-algebra determining all interaction vertices.

Identified the algebra as of pre-Calabi-Yau type, related to formality formalisms.

Connected algebraic products to integrals over convex polygons configuration spaces.

Abstract

Chiral Higher Spin Gravity is the minimal extension of the graviton with propagating massless higher spin fields. It admits any value of the cosmological constant, including zero. Its existence implies that Chern-Simons vector models have closed subsectors and supports the $3d$ bosonization duality. In this letter, we explicitly construct an $A_\infty$-algebra that determines all interaction vertices of the theory. The algebra turns out to be of pre-Calabi-Yau type. The corresponding products, some of which originate from Shoikhet-Tsygan-Kontsevich formality, are given by integrals over the configuration space of convex polygons.