Superstring BRST Cohomology

TL;DR

This paper analyzes the BRST cohomology of NSR superstring models with (1,1) supersymmetry, showing their cohomology groups are isomorphic to those of bosonic string models, thus linking their symmetries and anomalies.

Contribution

It derives all relevant world-sheet action functionals for these superstring models and proves the isomorphism of their BRST cohomology groups with bosonic models.

Findings

BRST cohomology groups for superstring models match those of bosonic strings for ghost number less than 4

Nontrivial symmetries and anomalies correspond between superstring and bosonic models

Provides a unified understanding of symmetries across string theories

Abstract

We first derive all world-sheet action functionals for NSR superstring models with (1,1) supersymmetry and any number of abelian gauge fields, for gauge transformations of the standard form. Then we prove for these models that the BRST cohomology groups $H^g(s)$, $g<4$ (with the antifields taken into account) are isomorphic to those of the corresponding bosonic string models, whose cohomology is fully known. This implies that the nontrivial global symmetries, Noether currents, background charges, consistent deformations and candidate gauge anomalies of an NSR (1,1) superstring model are in one-to-one correspondence with their bosonic counterparts.