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

Journal of High Energy Physics, Aug 2018

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.

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G. Bruno De Luca, Gabriele Lo Monaco, Niall T. Macpherson, Alessandro Tomasiello, Oscar Varela. The geometry of $$\mathcal{N}=3$$ AdS4 in massive IIA, Journal of High Energy Physics, 2018, 133, DOI: 10.1007/JHEP08(2018)133