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.
Highlights
The geometry of the N = 3, SO(4)-invariant, AdS4 solution of massive type IIA supergravity that uplifts from the N = 3 vacuum of D = 4 N = 8 dyonic ISO(7) supergravity is investigated
This can be regarded as a warped generalisation of the usual twistor fibration geometry
Like in the D = 11 tri-Sasaki case, though, the SO(3) R-symmetry acts on the fibers of the N = 3 massive IIA solution
Summary
We are ready to give the complete, non-linear embedding of the dynamical SO(4)invariant sector of D = 4 N = 8 ISO(7) supergravity into massive type IIA. As discussed in [3], the embedding of the full N = 8 theory is naturally expressed, at the level of the IIA metric, dilaton and form potentials, in terms of the restricted, SL(7)-duality hierarchy introduced in [24].
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