Notes on Ramond-Ramond spinors and bispinors in double field theory

TL;DR

This paper explores the relationship between spinor and bispinor formulations of Ramond-Ramond fields in double field theory, providing a covariant connection and clarifying duality frame distinctions.

Contribution

It introduces a covariant method to relate spinor and bispinor descriptions of Ramond-Ramond fields in DFT using a spinorial vielbein, and clarifies duality frame distinctions.

Findings

Established a covariant connection between spinor and bispinor formulations.

Elaborated on bispinor details in various dimensions and duality frames.

Clarified the distinction between IIA, IIB, and their duality frames.

Abstract

The Ramond-Ramond sector of double field theory (DFT) can be described either as an O(D,D) spinor or an O(D-1,1) x O(1,D-1) bispinor. Both formulations may be related to the standard polyform expansion in terms of even or odd rank field strengths corresponding to IIA or IIB duality frames. The spinor approach is natural in a (bosonic) metric formulation of DFT, while the bispinor is indispensable for supersymmetric DFT. In these notes, we show how these two approaches may be covariantly connected using a spinorial version of the DFT vielbein, which flattens an O(D,D) spinor into a bispinor. We also elaborate on details of the bispinor formulation in both even and odd D and elaborate on the distinction between the IIA/IIB/IIA*/IIB* duality frames.