T-duality in Ramond–Ramond backgrounds

Raphael Benichou,Giuseppe Policastro,Jan Troost

doi:10.1016/j.physletb.2008.01.059

Abstract

Using the pure spinor formalism on the world-sheet, we derive the T-duality rules for all target space couplings in an efficient manner. The world-sheet path integral derivation is a proof of the equivalence of the T-dual Ramond–Ramond backgrounds which is valid non-perturbatively in the string length over the curvature radius and to all orders in perturbation theory in the string coupling.

Highlights

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
The map between T-dual backgrounds was derived in a world-sheet path integral formalism for Neveu-Schwarz NeveuSchwarz fields in [3]
In [5] arguments were given for the transformation of the spacetime supersymmetry parameters, and the transformations of the gravitini and of the Ramond-Ramond fields were inferred by demanding compatibility between T-duality and supersymmetry

Summary

Introduction

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. The map between T-dual backgrounds was derived in a world-sheet path integral formalism for Neveu-Schwarz NeveuSchwarz fields in [3]. 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]. We give a novel world-sheet derivation of T-duality based on the pure spinor formalism [9]. 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, 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

Derivation of the classical T-duality rules

Regularization and quantum equivalence

Conclusions