On the Picture Dependence of Ramond-Ramond Cohomology

Closed string physical states are BRST cohomology classes computed on the space of states annihilated by $b_0^-$. Since $b_0^-$ does not commute with the operations of picture changing, BRST cohomologies at different pictures need not agree. We show explicitly that Ramond-Ramond (RR) zero-momentum physical states are inequivalent at different pictures, and prove that non-zero momentum physical states are equivalent in all pictures. We find that D-brane states represent BRST classes that are nonpolynomial on the superghost zero modes, while RR gauge fields appear as polynomial BRST classes. We also prove that in $x$-cohomology, the cohomology where the zero mode of the spatial coordinates is included, there is a unique ghost-number one BRST class responsible for the Green-Schwarz anomaly, and a unique ghost number minus one BRST class associated with RR charge.