Super Chern-Simons theory: Batalin-Vilkovisky formalism and A∞ algebras

This is a companion paper of a long work appeared in [C. Cremonini and P. Grassi, Pictures from super Chern-Simons theory, J. High Energy Phys. 03 (2020) 043JHEPFG1029-847910.1007/JHEP03(2020)043] discussing the super-Chern-Simons theory on supermanifolds. Here, it is emphasized that the Batalin-Vilkovisky formalism is naturally formulated using integral forms for any supersymmetric and supergravity models and we show how to deal with A∞ algebras emerging from supermanifold structures.