SO(d,d) Transformations of Ramond-Ramond Fields and Space-time Spinors

TL;DR

This paper explicitly constructs SO(d,d) transformations of Ramond-Ramond fields and space-time spinors in type-II theories, including cases involving the time direction, ensuring compatibility with supersymmetry and equations of motion.

Contribution

It provides a detailed derivation of SO(d,d) transformations for R-R fields and spinors, clarifying their relation to spinor representations and supersymmetry in type-II theories.

Findings

Explicit SO(d,d) transformations for R-R fields and potentials.

Inclusion of transformations involving the time direction.

Compatibility with space-time supersymmetry and equations of motion.

Abstract

We explicitly construct the SO(d,d) transformations of Ramond-Ramond field strengths and potentials, along with those of the space-time supersymmetry parameters, the gravitinos and the dilatinos in type-II theories. The results include the case when the SO(d,d) transformation involves the time direction. The derivation is based on the compatibility of SO(d,d) transformations with space-time supersymmetry, which automatically guarantees compatibility with the equations of motion. It involves constructing the spinor representation of a twist that an SO(d,d) action induces between the local Lorentz frames associated with the left- and right-moving sectors of the worldsheet theory. The relation to the transformation of R-R potentials as SO(d,d) spinors is also clarified.