Gauging Cosets

TL;DR

This paper develops a method to gauge the raising and lowering generators of any Lie algebra, exemplified with SU(N), introducing a second BRST charge to handle ghost constraints and explain grading in superstring quantization.

Contribution

It introduces a novel approach to gauge Lie algebra generators using dual BRST charges, expanding the understanding of ghost constraints and grading in string theory.

Findings

Successfully gauges SU(N) Lie algebra generators

Introduces a second BRST charge to handle ghost constraints

Provides a group theoretical explanation for superstring grading

Abstract

We show how to gauge the set of raising and lowering generators of an arbitrary Lie algebra. We consider SU(N) as an example. The nilpotency of the BRST charge requires constraints on the ghosts associated to the raising and lowering generators. To remove these constraints we add further ghosts and we need a second BRST charge to obtain nontrivial cohomology. The second BRST operator yields a group theoretical explanation of the grading encountered in the covariant quantization of superstrings.