Action and BRST transformation
The action in flat space is:

(1)

where are matter fields and are pure spinor ghosts, and are their conjugate momenta.

It is useful to introduce the following notations (TODO: verify coefficients):

(2)

(3)

The BRST transformation is:

(4)

or in compact notations:

The corresponding conserved BRST charge is of the form:

(5)

where is some composed field built from .