Geometries with Killing Spinors and Supersymmetric AdS Solutions

TL;DR

This paper explores special geometries with Killing spinors related to supersymmetric AdS solutions, generalizing known cases to higher odd dimensions and providing explicit examples.

Contribution

It introduces a new class of complex geometries in higher odd dimensions with Killing spinors, extending the understanding of supersymmetric AdS geometries.

Findings

Generalized geometries to higher odd dimensions with Killing spinors.

Constructed explicit examples for all dimensions considered.

Connected new geometries to known Sasaki-Einstein and AdS solutions.

Abstract

The seven and nine dimensional geometries associated with certain classes of supersymmetric $AdS_3$ and $AdS_2$ solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further elucidate their properties and also generalise them to higher odd dimensions by introducing a new class of complex geometries in $2n+2$ dimensions, specified by a Riemannian metric, a scalar field and a closed three-form, which admit a particular kind of Killing spinor. In particular, for $n\ge 3$, we show that when the geometry in $2n+2$ dimensions is a cone we obtain a class of geometries in $2n+1$ dimensions, specified by a Riemannian metric, a scalar field and a closed two-form, which includes the seven and nine-dimensional geometries mentioned above when $n=3,4$, respectively. We also consider various ansatz for the geometries and construct infinite classes of explicit examples for all $n$.