Dictionary for the type II nongeometric flux compactifications

TL;DR

This paper develops a comprehensive framework for understanding T-duality in type II flux compactifications, introducing axionic flux polynomials and mapping effective potentials between IIA and IIB theories.

Contribution

It introduces axionic flux polynomials and explicitly maps the effective potentials, fluxes, and Bianchi identities under T-duality in type II compactifications.

Findings

Explicit T-duality mapping between IIA and IIB fluxes and potentials

Introduction of axionic flux polynomials for concise potential representation

Demonstration of the framework with phenomenological examples

Abstract

We study the $T$-dual completion of the four-dimensional ${\cal N}=1$ 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 the 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 as well as the Bianchi identities of the two theories. Secondly, we propose what we call a set of "axionic flux polynomials", which depend on all the axionic moduli and the fluxes. This subsequently helps in presenting 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.