The geometry of mathcal{N}=3 AdS4 in massive IIA

Abstract

The geometry of the mathcal{N}=3 , SO(4)-invariant, AdS4 solution of massive type IIA supergravity that uplifts from the mathcal{N}=3 vacuum of D = 4 mathcal{N}=8 dyonic ISO(7) supergravity is investigated. Firstly, a D = 4, SO(4)-invariant restricted duality hierarchy is constructed and used to uplift the entire, dynamical SO(4)-invariant sector to massive type IIA. The resulting consistent uplift formulae are used to obtain a new local expression for the mathcal{N}=3 AdS4 solution in massive IIA and analyse its geometry. Locally, the internal S6 geometry corresponds to a warped fibration of S2 and a hemisphere of S4. This can be regarded as a warped generalisation of the usual twistor fibration geometry. Finally, the triplet of Killing spinors corresponding to the mathcal{N}=3 solution are constructed and shown to obey the massive type IIA Killing spinor equations.