Gaugings at angles from orientifold reductions

TL;DR

The paper identifies gaugings at angles as a key ingredient for moduli stabilisation in ${\cal N}=4$ gauged supergravity and shows that such gaugings arise naturally from orientifold reductions. By analyzing a tractable ${\cal N}=4$ truncation and a corresponding IIA orientifold reduction with fluxes, the authors obtain a ${CSO}(1,0,3)\times {CSO}(1,0,3)$ gauge structure with two independent $SL(2)$ angles, and a scalar potential that is a sum of two positive squares under a tadpole constraint $g_0 h_3 = N$. This work links the top-down string construction to bottom-up supergravity gaugings, clarifying how higher-dimensional origins can produce the angular gaugings essential for moduli stabilisation and potentially controlled vacua. It also suggests dual descriptions (e.g., IIB with O3-planes) and outlines future directions involving richer fluxes and geometric or non-geometric backgrounds to explore broader classes of stable or phenomenologically relevant vacua.

Abstract

We consider orientifold reductions to N=4 gauged supergravity in four dimensions. A special feature of this theory is that different factors of the gauge group can have relative angles with respect to the electro-magnetic SL(2) symmetry. These are crucial for moduli stabilisation and De Sitter vacua. We show how such gaugings at angles generically arise in orientifold reductions.