General Operator Solutions and BRST Quantization of Superstrings in the pp-Wave with Torsion

TL;DR

This paper presents a complete covariant quantization of superstrings in a pp-wave background with torsion, deriving operator solutions, anomaly calculations, and spacetime dimension constraints using BRST methods.

Contribution

It introduces a method for covariant quantization of superstrings in a flux background with torsion, including explicit operator solutions and anomaly analysis.

Findings

Derived covariant operator solutions satisfying equations of motion and (anti)commutation relations.

Calculated the super-Virasoro algebra anomaly in the flux background.

Determined spacetime dimensions and BRST constant from nilpotency conditions.

Abstract

We completely accomplish the canonically covariant quantization of Ramond-Neveu-Schwarz (RNS) superstrings in the pp-wave background with a non-zero flux of the NS-NS antisymmetric two-form field. Here this flux is equivalent to a nonvanishing torsion. In this quantization, general operator solutions, which satisfy the entire equation of motion and all the canonical (anti)commutation relations, play an important role. The whole of covariant string coordinates and fermions can be composed of free modes. Moreover, employing covariant free-mode representations, we calculate the anomaly in the super-Virasoro algebra and determine the number of dimensions of spacetime and the ordering constant from the nilpotency condition of the BRST charge in the pp-wave background with the flux.