Consistent truncations from duality symmetries and desingularization of orbifold uplifts

A bstract This paper is an extension of the results presented in [1]. We study G S -invariant subsectors of maximal gauged supergravities and show that such models can provide consistent truncations even when G S is not a symmetry of the original supergravity. We show that this construction is key to building pure supergravities around a supersymmetric AdS D solution. We illustrate this construction by building a consistent 𝒩 = 4 subsector of the D = 4 𝒩 = 8 [SO(6) × SO(1, 1)] ⋉ ℝ 12 gauged supergravity. We use this result to build the uplift of the multicharge spindle solutions in type IIB and we define a simple criterion for assessing the regularity of the uplift. We show that the type IIB uplift of the spindle is always non-regular, admitting eight codimension-six orbifold singularities. We apply the same criterion to other spindle uplifts, recovering known results and making predictions on the regularity of spindles on (quasi-)regular SE 7 manifolds.