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.