Covariant Quantization of Superstrings Without Pure Spinor Constraints

TL;DR

This paper develops a covariant quantization method for superstrings by introducing new ghosts to remove pure spinor constraints, resulting in a consistent BRST charge and correct massless spectrum.

Contribution

It extends Berkovits' approach by relaxing pure spinor constraints with new ghosts, enabling covariant quantization without anomalies.

Findings

Constructed a nilpotent BRST current

Achieved an anomaly-free energy-momentum tensor

Obtained the correct massless spectrum for open superstrings

Abstract

We construct a covariant quantum superstring, extending Berkovits' approach by introducing new ghosts to relax the pure spinor constraints. The central charge of the underlying Kac-Moody algebra, which would lead to an anomaly in the BRST charge, is treated as a new generator with a new b-c system. We construct a nilpotent BRST current, an anomalous ghost current and an anomaly-free energy-momentum tensor. For open superstrings, we find the correct massless spectrum. In addition, we construct a Lorentz invariant B-field to be used for the computation of the integrated vertex operators and amplitudes.