The no-ghost theorem for string theory in curved backgrounds with a flat timelike direction

TL;DR

This paper extends the no-ghost theorem to string theory in curved backgrounds with a flat timelike dimension, specifically proving it for the case where only the timelike direction is flat, using advanced algebraic techniques.

Contribution

It provides a proof of the no-ghost theorem for string backgrounds with a single flat timelike dimension, filling a gap in the understanding of string consistency in curved spacetimes.

Findings

Proves the no-ghost theorem for d=1 case.

Utilizes Frenkel-Garland-Zuckerman technique.

Extends known results to new background configurations.

Abstract

It is well-known that the standard no-ghost theorem can be extended straightforwardly to the general c=26 CFT on R^{d-1,1} \times K, where 2 \leq d \leq 26 and K is a compact unitary CFT of appropriate central charge. We prove the no-ghost theorem for d=1, i.e., when only the timelike direction is flat. This is done using the technique of Frenkel, Garland and Zuckerman.