On the cohomology and inner products of the Berkovits superparticle and superstring

TL;DR

This paper analyzes the complete cohomology of the Berkovits BRST operator for the superparticle, deriving an inner product consistent with string amplitudes and discussing a superspace covariant action for D=10 super Yang-Mills.

Contribution

It provides a detailed cohomology analysis of the Berkovits BRST operator and derives an inner product aligned with string amplitude prescriptions.

Findings

Cohomology is non-zero at eight ghost numbers, forming two isomorphic quartets.

Derived an inner product consistent with Berkovits' conjecture for string amplitudes.

Presented a manifestly superspace covariant Chern-Simons style action for D=10 super Yang-Mills.

Abstract

We describe the complete cohomology of the Berkovits BRST operator for the superparticle. It is non-zero at eight ghost numbers, splitting into two quartets, the members of each quartet being completely isomorphic. Based only on considerations of the isomorphisms of the cohomology, and using only the standard inner product, we derive the inner product appropriate for string amplitudes. It is in agreement with Berkovits' conjectured prescription, which is one element of an equivalence class. We discuss the Chern-Simons style action for D=10 super Yang-Mills, which is now manifestly superspace covariant.