T-duality in Ramond-Ramond backgrounds

Target space duality is a symmetry of string theory that maps a string theory in a background to a dual string theory in a dual background. For reviews see [1][2]. The map between T-dual backgrounds was derived in a world-sheet path integral formalism for Neveu-Schwarz NeveuSchwarz fields in [3]. For Ramond-Ramond backgrounds in type II, various derivations have appeared in the literature: the authors of [4] used the equivalence of the type II supergravity actions after reduction to nine dimensions. In [5] arguments were given for the transformation of the spacetime supersymmetry parameters, and then the transformations of the gravitini and of the Ramond-Ramond fields were inferred by demanding compatibility between T-duality and supersymmetry. A world-sheet derivation was obtained in the Green-Schwarz formalism in [6] up to quadratic order in the superspace coordinate, and later extended to all orders in [7][8]. In the present letter, we give a novel world-sheet derivation of T-duality based on the pure spinor formalism [9]. Our motivation for revisiting this problem is twofold: first, the duality rules are derived in a simpler and more streamlined way than with other methods. Secondly, since the pure spinor formalism gives a satisfactory conformal field theory description of the string in generic backgrounds, we are able to promote the duality to the path integral level, thus providing for a derivation of T-duality which is valid non-perturbatively in the string length over the curvature radius and to all orders in the string coupling. The duality is valid in the presence of Ramond-Ramond and fermionic backgrounds.