Cohomology ring of the BRST operator associated to the sum of two pure spinors

TL;DR

This paper investigates the algebraic structure of the cohomology ring associated with the BRST operator for the sum of two pure spinors in superstring theory, revealing its finite-dimensional algebraic properties.

Contribution

It provides a detailed analysis of the multiplicative structure of the cohomology ring related to the BRST complex for two pure spinors, a novel aspect in superstring theory.

Findings

The cohomology is an infinite-dimensional vector space but forms a finite-dimensional algebra.

The multiplicative structure of this algebra is explicitly characterized.

The cohomology ring is a finite-dimensional algebra over functions of a single pure spinor.

Abstract

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure.