On the BRST Operator Structure of the N=2 String

TL;DR

This paper analyzes the BRST operator cohomology in N=2 supergravity coupled to matter, revealing its structure at various ghost numbers and its relation to twisted superconformal symmetry.

Contribution

It provides a detailed cohomology analysis of the BRST operator in N=2 string theory, including descent equations and symmetry structures.

Findings

One cohomology class at ghost number one

Two independent classes at ghost number two

Conjecture of a class at ghost number three

Abstract

The BRST operator cohomology of $N=2$ $2d$ supergravity coupled to matter is presented. Descent equations for primary superfields of the matter sector are derived. We find one copy of the cohomology at ghost number one, two independent copies at ghost number two, and conjecture that there is a copy at ghost number three. The $N=2$ string has a twisted $N=4$ superconformal symmetry generated by the $N=2$ superstress tensor, the BRST supercurrent, the antighost superfield, and the ghost number supercurrent.