Closed strings in Ramond-Ramond backgrounds

We write the IIB Green-Schwarz action in certain general classes of curved backgrounds threaded with Ramond-Ramond fluxes. The fixing of the kappa symmetry in the light-cone gauge and the use of supergravity Bianchi identities simplify the task. We find an expression that truncates to quartic order in the spacetime spinors and relays interesting information about the vacuum structure of the worldsheet theory. The results are particularly useful in exploring integrable string dynamics in the context of the holographic duality.Comment: 24 pages; this is a significant revision to hep-th/0112063 with new results added, and including comparison with recent literature; v2: minor typos corrected, citations adde