Batalin-Vilkovisky algebras and two-dimensional topological field theories

Details Batalin-Vilkovisky algebras and two-dimensional topological field theories Batalin-Vilkovisky algebras and two-dimensional topological field theories

1992-12-07

arxiv.org/abs/hep-th/9212043v3

Commun.Math.Phys.159:265-285,1994

Physics

High Energy Physics

High Energy Physics - Theory

23 pages (Revised in many small ways.)

Scientific paper

10.1007/BF02102639

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.

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