Superstring BRST no-ghost theorem at arbitrary picture number

TL;DR

This paper provides a comprehensive and self-contained proof of the superstring BRST no-ghost theorem at arbitrary picture number, establishing the isomorphism of cohomology with the light-cone spectrum and constructing relevant pairings.

Contribution

It introduces a novel, simplified proof of the superstring BRST no-ghost theorem applicable at any picture number using spectral sequences.

Findings

Proves isomorphism between BRST cohomology and light-cone spectrum

Constructs pairings and inner products on cohomology

Provides a self-contained treatment at non-zero momentum

Abstract

A simple and self-contained treatment of the superstring BRST no-ghost theorem at non-zero momentum and arbitrary picture number is presented. We prove by applying the spectral sequence that the absolute BRST cohomology is isomorphic to two copies of the light-cone spectrum at adjacent ghost numbers. We single out a representative in each cohomology class. A non-degenerate pairing between the Fock spaces, an induced pairing on the cohomology and a Hermitian inner product on the cohomology are constructed.