On the N=2 Superstring BRST Operator

TL;DR

This paper presents a new expression for the N=2 superstring BRST operator, providing a straightforward proof of its nilpotence, which is fundamental for the consistency of the theory.

Contribution

The paper introduces a novel exponential form of the N=2 superstring BRST operator that simplifies the proof of its nilpotence.

Findings

The BRST operator can be expressed as a conjugation of a contour integral involving ghosts.

This form offers a trivial proof of the operator's nilpotence.

The approach clarifies the algebraic structure of the superstring BRST charge.

Abstract

We write the BRST operator of the N=2 superstring as $Q= e^{-R} (\oint \frac{dz}{2\pi i} ~ b \gamma_+ \gamma_-)e^R$ where $b$ and $gamma_\pm$ are super-reparameterization ghosts. This provides a trivial proof of the nilpotence of this operator.