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High Energy Physics - Theory, hep-th
Abstract:
The geometry of the ${\cal N} = 3$, SO(4)--invariant, AdS$_4$ solution of
massive type IIA supergravity that uplifts from the ${\cal N} = 3 $ vacuum of
$D=4$ ${\cal N} = 8$ 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 ${\cal 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 ${\cal N}=3$ solution are constructed and
shown to obey the massive type IIA Killing spinor equations.
