The Covariant Quantum Superstring and Superparticle from their Classical Actions

TL;DR

This paper develops a Noether-based method to construct BRST charges and invariant actions for covariant superstrings and superparticles, clarifying gauge fixing and cohomology in these theories.

Contribution

It introduces a systematic approach to derive BRST structures for superstrings and superparticles from their classical actions, including ghost sector analysis.

Findings

Ghosts b, c_z are essential for gauge fixing in the superstring.

Cohomology of the superparticle is explicitly determined.

Results extend to combined left- and right-moving sectors of superstring.

Abstract

We develop an approach based on the Noether method to construct nilpotent BRST charges and BRST-invariant actions. We apply this approach first to the holomorphic part of the flat-space covariant superstring, and we find that the ghosts b, c_z which we introduced by hand in our earlier work, are needed to fix gauge symmetries of the ghost action. Then we apply this technique to the superparticle and determine its cohomology. Finally, we extend our results to the combined left- and right-moving sectors of the superstring.