Comments on T-dualities of Ramond-Ramond Potentials

TL;DR

This paper introduces new potentials combining R-R and NS-NS fields to clarify T-duality invariance in type II string theories, providing a straightforward proof of invariance and simplifying related expressions.

Contribution

It proposes a new set of potentials transforming as Majorana-Weyl spinors under SO(d, d; Z), making T-duality invariance of R-R sectors more transparent.

Findings

New potentials transform as Majorana-Weyl spinors.

Simplified expressions including Chern-Simons terms.

Proof of T-duality invariance for arbitrary degree forms.

Abstract

The type IIA/IIB effective actions compactified on T^d are known to be invariant under the T-duality group SO(d, d; Z) although the invariance of the R-R sector is not so direct to see. Inspired by a work of Brace, Morariu and Zumino,we introduce new potentials which are mixture of R-R potentials and the NS-NS 2-form in order to make the invariant structure of R-R sector more transparent. We give a simple proof that if these new potentials transform as a Majorana-Weyl spinor of SO(d, d; Z), the effective actions are indeed invariant under the T-duality group. The argument is made in such a way that it can apply to Kaluza-Klein forms of arbitrary degree. We also demonstrate that these new fields simplify all the expressions including the Chern-Simons term.