Closed string vertex operators with various ghost number

We construct closed string vertex operators with various ghost numbers in addition to the conventional ones, using the Faddeev-Popov procedure for the gauge fixing of the conformal Killing group, from matter primary fields. We find that these operators give solutions to the descent equations in the framework of the BRST formalism. Similarly, we also construct solutions to the descent equations for the dilaton vertex operator with the Lorentz covariant form. Using the unintegrated vertex operator of the dilaton with the ghost number three, we obtain the correct result of the tadpole amplitude on the disk, including a non-zero contribution from a BRST exact term which comes from a conformal transformation.
Comment: 1+24 pages, no figures; v2: added the affiliation of one author, corrected eq.(5.9), ref.[10], and minor typos