A simple BRST system with quadratically constrained ghosts

TL;DR

This paper introduces a simplified model of the Berkovits pure spinor superparticle, analyzing its cohomology and constructing a topological string B-model, providing insights into constrained ghost systems.

Contribution

It presents a toy model for the pure spinor superparticle with explicit cohomology analysis and a novel construction of the topological B-model from this simplified system.

Findings

Explicit expression for the `b'-field in the model

Cohomology analysis of the toy model

Construction of the topological B-model from the system

Abstract

I present a toy model for the Berkovits pure spinor superparticle. It is a D=1, N=2 superparticle with no physical degrees of freedom. We study the cohomology in various ways, in particular finding an explicit expression for the `b'-field. Finally, we construct the topological string B-model from a straightforward generalization of the system.