Adding fluxes to consistent truncations: IIB supergravity on AdS ₃ × S ³ × S ³ × S ¹

We use E ₈₍₈₎ Exceptional Field Theory to construct the consistent truncation of IIB supergravity on S ³ × S ³ × S ¹ to maximal 3-dimensional N = 16 gauged supergravity containing the N = (4, 4) AdS ₃ vacuum. We explain how to achieve this by adding a 7-form flux to the S ¹ reduction of the dyonic E ₇₍₇₎ truncation on S ³ × S ³ previously constructed in the literature. Our truncation Ansatz includes, in addition to the N = (4, 4) vacuum, a host of moduli breaking some or all of the supersymmetries. We explicitly construct the uplift of a subset of these to construct new supersymmetric and non-supersymmetric AdS ₃ vacua of IIB string theory, which include a range of perturbatively stable non-supersymmetric 10-d vacua. Moreover, we show how the supersymmetric direction of the moduli space of AdS ₃ vacua of six-dimensional gauged supergravity studied in [1] is compactified upon lifting to 10 dimensions, and find evidence of T-duality playing a role in global aspects of the moduli space. Along the way, we also derive the form of 3-dimensional N = 16 gauged supergravity in terms of the embedding tensor and rule out a 10-/11-dimensional origin of some 3-dimensional gauged supergravities.