Comments on T-Dualities of Ramond-Ramond Potentials

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 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 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. * )

Duality twisted reductions of Double Field Theory of Type II strings

“…The aim of this subsection is to give a brief review of the democratic formulation of the bosonic sector of (massless) Type IIA and Type IIB supergravity theories [48,49] (also see [50,51]). The (bosonic) matter content of these two theories are as follows:…”

“…It can be shown that the actions given above are equivalent to the standard action of Type IIA and Type IIB supergravity theories, which also involve some complicated Chern-Simons type terms, in the following sense [37,48,49]: if one applies the duality relations (3.6) to the field equations derived from the actions (3.8), (3.9), then one obtains exactly the same field equations that one would have derived from the standard actions. The field equations for lower degree form fields match directly in the two formulations.…”

“…This immediately tells us that the modified RR fields transform in the spin representation of the group SO(n, n) or Spin(n, n). In fact, the main motivation of constructing the democratic formulation in the first place was to show the invariance of the RR sector under the orthogonal group [48]. In order to achieve this, one reduces Type IIA or Type IIB on a ( 10 The main purpose of this section is to give a brief overview of DFT and in particular, to review how the sector of DFT describing the RR fields is an extension of the democratic formulation of Type II theories, in the sense that it reduces exactly to it in a particular frame.…”

New examples of flux vacua

“…The R-R potentials are implicitly defined by (B.3). T-duality acts on these field strengths as follows [61][62][63][64]51], The virtue of using this definition is the ability to dualize backgrounds for which the R-R field strengths respect the chosen isometries, while the associated R-R potentials need not. …”

Supersymmetry and the systematics of T-duality rotations in type-II superstring theories

“…More recently, the case of single T-duality in the presence of supersymmetry has also been considered in [5][6][7]. In [8,9] it was observed that the potentials C ′(n) transform in the spinor representations of the Tduality group, verified directly in [10]. Also, see [11].…”