On Type IIA AdS3 solutions and massive GK geometries

Abstract

Abstract We give necessary and sufficient conditions for warped AdS3 (and Mink3) solutions of Type II supergravities to preserve 𝒩 = (2, 0) supersymmetry, in terms of geometric conditions on their internal space M7. Such solutions possess a canonical ten-dimensional 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 M7 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 M7 becomes 𝕋2 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 AdS3 solutions to preserve arbitrary extended chiral supersymmetry.