Deformations of action and of BRST structureUsually the BRST-invariant deformations of the worldsheet action are accompanied by the corresponding deformation of the BRST operator . The deformations of the BRST structure are tied to the deformations of the action. For example, let us look at the -deformation:As we already explained, for the undeformed action .What happens when we add our current-current deformation? We use:and then we use the equation of motion to show that the variation of is zero. In other words, the BRST variation of is zero only on-shell.This means that:

the deformed action does have a BRST structure, but:

we have to remember that the BRST operator is not the same as it was in flat space: