Batalin-Vilkovisky formality for Chern-Simons theory

TL;DR

This paper proves that the differential graded Lie algebra of functionals in Chern-Simons theory is homotopy abelian, providing insights into the algebraic structure of field theories within the Batalin-Vilkovisky formalism.

Contribution

It establishes the homotopy abelian property of the functional algebra in Chern-Simons theory and generalizes the variational complex as a differential graded Lie algebra.

Findings

The functional algebra in Chern-Simons theory is homotopy abelian.

The variational complex in BV formalism forms a differential graded Lie algebra.

Provides a framework for understanding algebraic structures in field theories.

Abstract

We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. For a general field theory, we show that the variational complex in the Batalin-Vilkovisky formalism is a differential graded Lie algebra.