We interpret Eq. (7) as a requirement that the OPE of the integrated vertex operator with the -ghost be BRST-exact up to a total derivative.

This is a vague statement, which requires proof. For bosonic string:

Let us consder a special case when is holomorphic (only depends on ). In this case generates a symmetry of the classical action (shift of the -ghost ). The Noether charge of this symmetry is . Therefore, corresponds to the OPE with .

It was pointed out by Nelson that and could be non-zero. Only their difference (denoted ) should be zero. This is because, in order to define the integration over the moduli space, we do not actually need the integration form to be completely horizonthal. There is some partial canonical gauge fixing.