T-Duality, Space-time Spinors and R-R Fields in Curved Backgrounds

TL;DR

The paper analyzes T-duality in Type-II string theories on curved backgrounds with isometries, showing that duality acts not only on space-time indices but also twists the left-moving local Lorentz frame, which induces a well-defined transformation on space-time spinors. By deriving explicit, exact linear-order relations for the supersymmetry parameters, gravitinos, and dilatinos, the work obtains the corresponding T-duality rules for Ramond-Ramond fields and potentials, including the massive IIA case via a locality-preserving hat{C} construction. The results unify the treatment of spinor and RR-field dualities in curved backgrounds and provide a simple derivation of the mass-dependent Wess-Zumino terms on D-brane worldvolumes, highlighting the role of worldsheet sector mixing in non-self-dual backgrounds. The framework clarifies the interplay between left-right frame twists, RR-duality, and D-brane couplings, with potential extensions to broader duality groups such as $SO(d,d)$ in low-energy effective theories. Overall, the paper offers a cohesive, spinor-centered perspective on T-duality in curved spaces and its impact on RR fields and brane actions.

Abstract

We obtain the T-duality transformations of space-time spinors (the supersymmetry transformation parameters, gravitinos and dilatinos) of type-II theories in curved backgrounds with an isometry. The transformation of the spinor index is shown to be a consequence of the twist that T-duality introduces between the left and right-moving local Lorentz frames. The result is then used to derive the T-duality action on Ramond-Ramond field strengths and potentials in a simple way. We also discuss the massive IIA theory and, using duality, give a short derivation of ``mass''-dependent terms in the Wess-Zumino actions on the D-brane worldvolumes.