The Quantum Superstring as a WZNW Model with N=2 Superconformal Symmetry

TL;DR

This paper develops a covariant quantization method for superstrings in 10D using a gauged WZNW model with N=2 superconformal symmetry, avoiding manual ghost introduction and maintaining Lorentz covariance.

Contribution

It introduces a new covariant superstring quantization framework based on a gauged WZNW model with N=2 superconformal symmetry, featuring two BRST charges and no manual ghost insertion.

Findings

Model has vanishing central charge.

Physical states are in the cohomology of combined BRST charges.

Formalism is fully Lorentz covariant.

Abstract

We present a new development in our approach to the covariant quantization of superstrings in 10 dimensions which is based on a gauged WZNW model. To incorporate worldsheet diffeomorphisms we need the quartet of ghosts $(b_{zz},c^{z}, \b_{zz}, \g^{z})$ for topological gravity. The currents of this combined system form an N=2 superconformal algebra. The model has vanishing central charge and contains two anticommuting BRST charges, $Q_{S}=Q_{W} + \oint \g^{z} b_{zz} + \oint \eta_{z}$ and $Q_{V} = \oint c^{z} \Big(T^{W}_{zz} + {1\over 2} T^{top}_{zz}\Big) + \g^{z} (B^{W}_{zz} + {1\over 2} B^{top}_{zz} \Big)$, where $\eta_{z}$ is obtained by the usual fermionization of $\b_{zz}, \g^{z}$. Physical states form the cohomology of $Q_{S}+Q_{V}$, have nonnegative grading, and are annihilated by $b_{0}$ and $\beta_{0}$. We no longer introduce any ghosts by hand, and the formalism is completely Lorentz covariant.