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