On the Picture Dependence of Ramond-Ramond Cohomology

TL;DR

This paper investigates how Ramond-Ramond (RR) cohomology classes depend on the picture in string theory, revealing inequivalence at zero momentum and establishing unique classes related to anomalies and RR charge.

Contribution

It explicitly demonstrates picture dependence of RR zero-momentum states and identifies unique BRST classes linked to anomalies and RR charge.

Findings

RR zero-momentum states are inequivalent at different pictures.

Non-zero momentum states are equivalent across pictures.

Distinct BRST classes correspond to anomalies and RR charge.

Abstract

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.