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

Abstract

Abstract The geometry of the N=3 $$ \mathcal{N}=3 $$, SO(4)-invariant, AdS4 solution of massive type IIA supergravity that uplifts from the N=3 $$ \mathcal{N}=3 $$ vacuum of D = 4 N=8 $$ \mathcal{N}=8 $$ 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 N=3 $$ \mathcal{N}=3 $$ AdS4 solution in massive IIA and analyse its geometry. Locally, the internal S 6 geometry corresponds to a warped fibration of S 2 and a hemisphere of S 4. This can be regarded as a warped generalisation of the usual twistor fibration geometry. Finally, the triplet of Killing spinors corresponding to the N=3 $$ \mathcal{N}=3 $$ solution are constructed and shown to obey the massive type IIA Killing spinor equations.

Keywords

• AdS-CFT Correspondence
• Flux compactifications
• Supergravity Models
• Superstring Vacua