Superstring in the pp-wave background with RR flux as a conformal field theory

TL;DR

This paper formulates the superstring theory in a pp-wave background with RR flux as an exact conformal field theory, overcoming coupling challenges via a phase-space approach and establishing a consistent quantum Virasoro algebra.

Contribution

It introduces a phase-space formulation for superstrings in RR flux backgrounds, enabling the construction of quantum Virasoro generators and BRST analysis without relying on equations of motion.

Findings

Successfully constructed classical and quantum Virasoro generators

Demonstrated anomaly cancellation with proper normal ordering

Reproduced known physical spectrum via BRST cohomology

Abstract

We provide a concise description of our recent work on the exact conformal field theory (CFT) formulation of the superstring in the pp-wave background with Ramond-Ramond (RR) flux, using the Green-Schwarz formalism in the semi-light-cone conformal gauge. Due to the presence of the RR flux, the left- and the right-moving degrees of freedom on the worldsheet are inherently coupled and this makes the canonical analysis intractable even at the classical level. To overcome this difficulty, we develop a phase-space formulation which does not make use of the equations of motion, and construct two independent sets of Virasoro generators classically. Upon quantization, due to the presence of the RR flux, the Virasoro algebra generically develops quantum operator anomalies and only with a judicious choice of normal ordering rescription they cancel between the bosonic and the fermionic contributions. With such properly defined quantum Virasoro generators, one can construct the BRST operators and demonstrate that the BRST cohomology analysis reproduces the physical spectrum previously obtained in the light-cone gauge.