On the Covariant Quantization of Type II Superstrings

TL;DR

This paper advances covariant quantization of type II superstrings by reformulating a gauged WZNW model approach, clarifying the BRST structure, and revealing the necessity of additional ghosts for nilpotency.

Contribution

It provides a new off-shell, chirally split formulation of the covariant quantization method and constructs the free gauged WZNW action, simplifying previous supergroup manifold approaches.

Findings

Constructed the free action of the gauged WZNW model for type II superstrings.

Analyzed the BRST charges and their relation to the N=2 superconformal algebra.

Discovered that nilpotency of the BRST charge requires an extra quartet of ghosts.

Abstract

In a series of papers Grassi, Policastro, Porrati and van Nieuwenhuizen have introduced a new method to covariantly quantize the GS-superstring by constructing a resolution of the pure spinor constraint of Berkovits' approach. Their latest version is based on a gauged WZNW model and a definition of physical states in terms of relative cohomology groups. We first put the off-shell formulation of the type II version of their ideas into a chirally split form and directly construct the free action of the gauged WZNW model, thus circumventing some complications of the super group manifold approach to type II. Then we discuss the BRST charges that define the relative cohomology and the N=2 superconformal algebra. A surprising result is that nilpotency of the BRST charge requires the introduction of another quartet of ghosts.