Dictionary for the type II nongeometric flux compactifications

Abstract

We study the $T$-dual completion of the four-dimensional $\mathcal{N}=1$ type II effective potentials in the presence of (non)geometric fluxes. First, we invoke a cohomology version of the $T$-dual transformations among the various moduli, axions, and fluxes appearing in the type IIA and type IIB effective supergravities. This leads to some useful observations about a significant mixing of the standard NS-NS fluxes with the (non)geometric fluxes on the mirror side. Further, using our $T$-duality rules, we establish an explicit mapping among the $F$ terms, $D$ terms, tadpole conditions, and Bianchi identities of the two theories. Second, we propose what we call a set of ``axionic flux polynomials,'' which depend on all of the axionic moduli and the fluxes. This subsequently helps to present the two scalar potentials in a concise and manifestly $T$-dual form, which can be directly utilized for various phenomenological purposes, as we illustrate in a couple of examples.