N=2 structures in all string theories

TL;DR

This paper demonstrates that all string theories are cohomologically equivalent to twisted N=2 superconformal field theories, providing a unifying perspective through BRST cohomology and topological gravity coupling.

Contribution

It proves that any string theory's BRST cohomology aligns with that of a twisted N=2 superconformal field theory, supporting a broad conjecture in topological conformal field theory.

Findings

Cohomological equivalence between string theories and twisted N=2 SCFTs.

Construction of equivalence via coupling to topological gravity.

Evidence supporting the universality of 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. Let us say that two topological conformal field theories are ``cohomologically equivalent'' if their BRST cohomologies are isomorphic as Batalin--Vilkovisky algebras. What we show in this paper is 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 W_3 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 comments on different notions of equivalence for topological conformal field theories and this leads to an improved conjecture.