BRST complexIn Type IIB theory, there are two pure spinors and .where are the structure constants of ,The BRST complex computing supergravity excitations on the background is:where is the space of polynomials functions of the order of two independent pure spinors and :The space is the space of functions of and pure spinors , more precisely: Taylor series in and polynomials of the order in .

The is given by:Here is the left multiplication by .