More on Chiral Higher Spin Gravity and convex geometry

Recently, a unique class of local Higher Spin Gravities with propagating massless fields in 4d – Chiral Gravity was given covariant formulation both flat and (A)dS4 spacetimes at the level equations motion. We unfold corresponding homological perturbation theory as to explicitly obtain all interaction vertices. The vertices reveal remarkable simplicity after an appropriate change variables. Similarly formality theorems A?/L? multi-linear products can be represented integrals over configuration space, which our case is space convex polygons. A?-algebra underlying Theory pre-Calabi–Yau type. As consequence, motion have Poisson sigma-model form.