The geometry of $\mathcal{N}=3$ AdS${}_4$ in massive IIA

Abstract

The geometry of the $\mathcal{N}=3$, SO(4)--invariant, AdS${}_4$ 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 $\mathcal{N}=3$ AdS${}_4$ 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 $\mathcal{N}=3$ solution are constructed and shown to obey the massive type IIA Killing spinor equations.

arXiv comment43 pages. v2: References added and minor typos corrected. Version to be published in JHEP

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• AdS${}_3$ solutions with $\mathcal{N}=(3,0)$ from S${}^3\times$S${}^3$ fibrations
• Brane-jet stability of non-supersymmetric AdS vacua
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Flowing to $\mathcal{N}=3$ Chern--Simons-matter theory
• Supersymmetric spectroscopy on AdS${}_4\times S^7$ and AdS${}_4\times S^6$
• Super-Chern-Simons spectra from Exceptional Field Theory
• Constraining integrable AdS/CFT with factorized scattering
• Minimal $D=4$ truncations of type IIA
• Halving ISO(7) supergravity
• Mink${}_4\times S^2$ Solutions of 10 and 11 Dimensional Supergravity