On Type IIA AdS$_3$ solutions and massive GK geometries

Abstract

We give necessary and sufficient conditions for warped AdS 3 (and Mink 3 ) solutions of Type II supergravities to preserve N = (2, 0) supersymmetry, in terms of geometric conditions on their internal space M 7 . Such solutions possess a canonical d = 10 Killing vector that can be either time-like or null. In this work we classify the null case in massive Type IIA supergravity which necessitates that M 7 decomposes as a circle fibration over a six-dimensional base with orthogonal SU(2)-structure containing a complex four-manifold. We narrow our focus to solutions for which M 7 becomes T 2 fibred over a foliation of a Kähler manifold over an interval. We find a class of solutions which are the massive Type IIA version of GK geometries and present an extremal problem which computes the central charge of the solution using just topology. Finally, we present geometric conditions for AdS 3 solutions to preserve arbitrary extended chiral supersymmetry.

Black Holes from Branes

“…These were first constructed as 7d and 9d manifolds appearing in supersymmetric AdS 3 and AdS 2 solutions in type IIB and 11d supergravity respectively [105,138]. Later it was realized that the structure of these geometries can be generalized to arbitrary odd dimension (≥ 5) [139,149].…”