The no-ghost theorem in curved backgrounds with a timelike u(1): NSR string

TL;DR

This paper proves the no-ghost theorem for NSR strings in curved backgrounds with a timelike u(1) symmetry, extending previous results to more general settings using BRST quantization techniques.

Contribution

It extends the no-ghost theorem to NSR strings in backgrounds with a timelike u(1) SCFT, beyond flat light-cone directions, using BRST quantization methods.

Findings

The no-ghost theorem holds in curved backgrounds with a timelike u(1) symmetry.

The proof employs BRST quantization and techniques from Frenkel, Garland, and Zuckerman.

Applicable to backgrounds where the timelike direction forms a u(1) SCFT.

Abstract

It is well-known that the standard no-ghost theorem is valid as long as the background has the light-cone directions. We prove the no-ghost theorem for the NSR string when only the timelike direction is flat. This is done by the BRST quantization, using the technique of Frenkel, Garland and Zuckerman and our previous results for the bosonic string. The theorem actually applies as long as the timelike direction is written as a u(1) SCFT.