Deformations of action and of BRST structure

Usually 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: