I also want where and are separately nilpotent symmetries, and moreover is holomorphic and antiholomorphic.

And I want the action of algebraic tori: and (holomorphic and antiholomorphic). I want their orbits to go through the singular locus, by scaling the bosonic ghosts to zero. The idea is that the bosonic ghosts are “infinitesimal”. Everything infinitesimal can be scaled. (But they take values in the cone, not in a linear space.)

The BRST operators should be charged under and :