Batalin-Vilkovisky algebras and two-dimensional topological field theories

TL;DR

This paper demonstrates that the cohomology of two-dimensional topological field theories naturally possesses a Batalin-Vilkovisky algebra structure, connecting algebraic topology with quantum field theory insights.

Contribution

It establishes a natural Batalin-Vilkovisky algebra structure on the cohomology of 2D topological field theories using algebraic topology, complementing previous algebraic approaches.

Findings

Batalin-Vilkovisky structure exists on 2D topological field theory cohomology

The approach uses algebraic topology rather than algebraic methods

Supports previous results in 2D string theory context

Abstract

Batalin-Vilkovisky algebras are a new type of algebraic structure on graded vector spaces, which first arose in the work of Batalin and Vilkovisky on gauge fixing in quantum field theory. In this article, we show that there is a natural structure of a Batalin-Vilkovisky algebra on the cohomology of a topological field theory in two dimensions. Lian and Zuckerman have constructed this Batalin-Vilkovisky structure, in the setting of topological chiral field theories, and shown that the structure is non-trivial in two-dimensional string theory. Our approach is to use algebraic topology, whereas their proofs have a more algebraic character.