This means that the field configuration has the same action as for an arbitrary odd gauge parameter function on the worldsheet:

Locally and away from the fixed points of this implies that one of the target space fermionic coordinates completely decouples from the action (the action does not depend on it). In case of pure spinor sigma-model, this gauge symmetry does not account for all degeneracy of the action. All directions in the space tangent to the pure spinor cones are degenerate directions of the quadratic part of the action.

Let us add an additional scalar field on the worldsheet and consider the following solution of the Master Equation:

In the pure spinor case is parametrized by and , modulo rescaling ( i.e. projective pure spinors).

In Type II pure spinor theory, there are actually two anticommuting BRST symmetries, and , and the term in linear in antifields is

The action is given by Eq. (32). Such a theory requires regularization.

The minimalistic sigma-model action is written in terms of the target space metric and the B-field . For example, the action of Eq. (32) corresponds to:

The existence of the -ghost is equivalent to the metric being the Lie derivative along of some symmetric tensor :

where is the Lie derivative along the vector field . In our case (Appendix BRST variation of the -tensor):

As in Section The -ghost, the part of the action involving the target space metric is BRST exact.