Superstring Perturbation Theory and Ramond-Ramond Backgrounds

TL;DR

The paper develops a perturbative framework for Type II strings in RR backgrounds by summing over worldsheet boundaries and enforcing conformal invariance through the Fischler-Susskind mechanism, yielding a σ-model that incorporates RR fields. In the large-N limit, open-string loops generate a background geometry, with AdS_5 x S^5 in the near-horizon limit serving as a key example; the approach naturally produces backreaction consistent with supergravity equations of motion. It demonstrates RR/NSNS state mixing at leading order, and shows that spacetime supersymmetry can be realized on the worldsheet through modified currents and Killing-spinor constraints, suggesting a route toward an exact CFT description in RR backgrounds. This framework has implications for gauge/gravity duality and the perturbative treatment of D-brane geometries in covariant string theory.

Abstract

We consider perturbative Type II superstring theory in the covariant NSR formalism in the presence of NSNS and RR backgrounds. A concrete example that we have in mind is the geometry of D3-branes which in the near-horizon region is AdS_5 x S_5, although our methods may be applied to other backgrounds as well. We show how conformal invariance of the string path integral is maintained order by order in the number of holes. This procedure makes uses of the Fischler-Susskind mechanism to build up the background geometry. A simple formal expression is given for a σ-model Lagrangian. This suggests a perturbative expansion in 1/g^2N and 1/N. As applications, we consider at leading order the mixing of RR and NSNS states, and the realization of the spacetime supersymmetry algebra.