Linear dilaton

First of all, the “most leading” deformation actually has , i.e.
.
The action is not deformed.

What does get deformed is the BRST transformation. The deformation of the BRST charge is:

where and are the left and right SUSY transformations.
The corresponding unintegrated vertex is:

What happens is where is a conserved current.
Flat space superstring has a ghost number 1 conserved charge anticommuting with
(and different from ).
We are deforming the BRST transformation without deforming the action.