Type II supergravity origin of dyonic gaugings

Dyonic gaugings of four-dimensional supergravity typically exhibit a richer vacuum structure compared to their purely electric counterparts, but their higher-dimensional origin often remains more mysterious. We consider a class of dyonic gaugings with gauge groups of the type (SO(p, q) x SO (p', q')) proportional to N with N nilpotent. Using generalized Scherk-Schwarz reductions of exceptional field theory, we show how these four-dimensional gaugings may be consistently embedded in type II supergravity upon compactification around products of spheres and hyperboloids. As an application, we give the explicit uplift of the N = 4 AdS(4) vacuum of the theory with gauge group (SO(6) x SO (1, 1)) proportional to T(12)into a supersymmetric AdS(4) x M-5 x S-1 S-fold solution of IIB supergravity. The internal space M-5 is a squashed S-5 preserving an SO(4) subset of SO(6) subset of its isometries.