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

TL;DR

This paper derives how T-duality transforms space-time spinors, R-R fields, and potentials in curved backgrounds, clarifying the role of local Lorentz frames and extending to massive IIA theory and D-brane actions.

Contribution

It provides a detailed derivation of T-duality transformations for spinors and R-R fields in curved backgrounds with isometries, including massive IIA theory.

Findings

T-duality induces a twist between left and right-moving Lorentz frames.

Derived T-duality action on R-R field strengths and potentials.

Presented a short derivation of mass-dependent terms in D-brane Wess-Zumino 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.