Chiral higher spin gravity and convex geometry

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