N=4 Gauged Supergravity from Duality-Twist Compactifications of String Theory

TL;DR

The work addresses the problem of embedding half-maximal ${\cal N}=4$ gauged supergravities in string theory by implementing duality-twist reductions of heterotic string theory on $T^4$ and Type II string theory on $K3$. It develops a unified framework where fluxes and monodromies in $O(4,20;\mathbb{Z})$ realize geometric, non-geometric (T-fold), and Mirror-fold backgrounds, with explicit constructions of geometric $f$, $H$, and $F$-fluxes and non-geometric $Q$, $W$, and Mirror-fold fluxes. A six-dimensional intermediate theory with $O(4,20)$ symmetry is connected to the four-dimensional gauged supergravity via a $T^2$ duality twist, and a heterotic worldsheet description is provided through a doubled torus formalism. The results illuminate how non-geometric backgrounds can serve as credible string realizations of gauged supergravities and motivate further checks of heterotic/IIA duality in these generalized settings. Overall, the paper advances the understanding of string-compactification realizations of ${\cal N}=4$ gaugings and highlights the role of duality and non-geometric structures in modern string phenomenology.

Abstract

We investigate the lifting of half-maximal four-dimensional gauged supergravities to compactifications of string theory. It is shown that a class of such supergravities can arise from compactifications of IIA string theory on manifolds of SU(2)-structure which may be thought of as K3 fibrations over T^2. Examples of these SU(2)-structure backgrounds, as smooth K3 bundles and as compactifications with H-flux, are given and we also find evidence for a class of non-geometric, Mirror-fold backgrounds. By applying the duality between IIA string theory on K3 and Heterotic string theory on T^4 fibrewise, we argue that these SU(2)-structure backgrounds are dual to Heterotic compactifications on a class T^4 fibrations over T^2. Examples of these fibrations as twisted tori, H-flux and T-fold compactifications are given. We also construct a new set of backgrounds, particular to Heterotic string theory, which includes a previously unknown class of Heterotic T-folds. A sigma model description of these backgrounds, from the Heterotic perspective, is presented in which we generalize the Bosonic doubled formalism to Heterotic string theory.