Comments on T-dualities of Ramond-Ramond potentials

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 cannot be seen so directly. Inspired by a work of Brace, Morariu and Zumino, we introduce new potentials, which are mixtures of R-R potentials and the NS-NS a-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.