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.
Notice that is the ghost number one vertex corresponding to left SUSY transformation. Generally speaking:
ghost number one vertices correspond to global symmetries
For example, corresponds to
the Poincare translation.