Super Chern-Simons Theory: BV-formalism and $A_\infty$-algebras

TL;DR

This paper explores the formulation of super-Chern-Simons theory using BV formalism with integral forms and investigates the role of $A_ infty$-algebras arising from supermanifold structures, providing a mathematical framework for supersymmetric models.

Contribution

It introduces a natural BV formalism for super-Chern-Simons theory using integral forms and elucidates the emergence of $A_ infty$-algebras from supermanifold structures.

Findings

BV formalism is effectively formulated with integral forms for supersymmetric models

$A_ infty$-algebras naturally arise from supermanifold structures

Provides a mathematical framework linking supergeometry and gauge theories

Abstract

This is a companion paper of a long work appeared in [1] discussing the super-Chern-Simons theory on supermanifolds. Here, it is emphasized that the BV formalism is naturally formulated using integral forms for any supersymmetric and supergravity models and we show how to deal with $A_\infty$-algebras emerging from supermanifold structures.