Dictionary for the type II nongeometric flux compactifications

We study the T -dual completion of the four-dimensional 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.