2007/10/13 by Jerome P. Gauntlett, Nakwoo Kim
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.1007/s00220-008-0575-5
published as Commun.Math.Phys.284:897-918,2008 · 28 pages
arxiv created 2007/10/13 · openalex publication_date 2008/07/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The seven and nine dimensional geometries associated with certain classes of supersymmetric AdS3 and AdS2 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≥ 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.