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

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.

BRST cohomology of the sum of two pure spinors

We study the zero mode cohomology of the sum of two pure spinors. The knowledge of this cohomology allows us to better understand the structure of the massless vertex operator of the Type IIB pure spinor superstring.