N=2 structures in string theories

Abstract

The BRST cohomology of any topological conformal field theory admits the structure of a Batalin–Vilkovisky algebra, and string theories are no exception. Loosely speaking, we say that two topological conformal field theories are cohomologically equivalent if their BRST cohomologies are isomorphic as Batalin–Vilkovisky algebras. In this paper we argue that any string theory (regardless of the matter background) is cohomologically equivalent to some twisted N=2 superconformal field theory. We discuss three string theories in detail: the bosonic string, the NSR string and the W3 string. In each case the way the cohomological equivalence is constructed can be understood as coupling the topological conformal field theory to topological gravity. These results lend further supporting evidence to the conjecture that any topological conformal field theory is cohomologically equivalent to some topologically twisted N=2 superconformal field theory. We end the paper with some speculative comments on Massey products in topological conformal field theories.