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arXiv · 0710.2590

Geometries with Killing Spinors and Supersymmetric AdS Solutions

Jerome P. Gauntlett·Nakwoo Kim
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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 $n$.

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Jerome P. Gauntlett, Nakwoo Kim. 2007-10-13. Geometries with Killing Spinors and Supersymmetric AdS Solutions. https://doi.org/10.1007/s00220-008-0575-5

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