In Type IIB theory, there are two pure spinors
and
.
| (34) |
where
are the structure constants of
,
The BRST complex computing supergravity excitations on the background
is:
| (35) |
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:
| (36) |
Here
is the left multiplication by
.