Improved Proof of the No-ghost Theorem for Fermion States of the Superstring

TL;DR

This paper extends an improved proof of the no-ghost theorem to the Ramond fermion string, using a super-Virasoro algebra basis, and calculates the BRST cohomology for the system.

Contribution

It provides the first self-contained proof of the no-ghost theorem for the Ramond fermion string using an efficient basis and super-Virasoro algebra.

Findings

Established linear independence of basis elements

Extended proof to Ramond fermion string

Calculated BRST cohomology for the system

Abstract

The purpose of this note is to extend the improved proof of the no-ghost theorem for the bosonic and Neveu-Schwarz dual resonance models, presented in my article Nuclear Physics B286 (1987) 61, to cover the Ramond fermion string. As in that paper, the improvement involves the identification of an efficient basis for string state space and a self-contained proof, based on the super-Virasoro algebra, of the linear independence of the basis elements. We use our results to calculate the BRST cohomology for this system.