Superstring Perturbation Theory and Ramond-Ramond Backgrounds

TL;DR

This paper develops a perturbative approach to superstring theory in backgrounds with Ramond-Ramond fields, ensuring conformal invariance and exploring implications for D3-brane geometries and supersymmetry.

Contribution

It introduces a method to maintain conformal invariance in superstring perturbation theory with RR backgrounds using the Fischler-Susskind mechanism, applicable to D-brane geometries.

Findings

Conformal invariance preserved order by order in string perturbation.

Derived a formal expression for the sigma-model Lagrangian in RR backgrounds.

Analyzed mixing of RR and NSNS states and supersymmetry realization.

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 \sigma-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.