Geometries with Killing Spinors and Supersymmetric AdS Solutions

Abstract

The seven and nine dimensional geometries associated with certain classes of supersymmetric $Ad{S}_3$ and $Ad{S}_2$ 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 $n$.

28 pages

References in corpus (23)

• Supergravity description of field theories on curved manifolds and a no go theorem
• Bubbling AdS space and 1/2 BPS geometries
• The Exact Superconformal R-Symmetry Maximizes a
• On Flux Quantization In M-Theory And The Effective Action
• Superstrings with Intrinsic Torsion
• The Geometry of D=11 Killing Spinors
• G-Structures and Wrapped NS5-Branes
• Sasaki-Einstein Manifolds and Volume Minimisation
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• Supersymmetry of Anti-de Sitter Black Holes
• AdS(3) Solutions of IIB Supergravity from D3-branes
• Supersymmetric AdS_3, AdS_2 and Bubble Solutions
• Ricci-flat Metrics, Harmonic Forms and Brane Resolutions
• Supersymmetry of Black Strings in D=5 Gauged Supergravities
• The general form of supersymmetric solutions of N=(1,0) U(1) and SU(2) gauged supergravities in six dimensions
• Membranes Wrapped on Holomorphic Curves
• Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity
• Comments on AdS2 solutions of D=11 Supergravity
• BPS Geometries and AdS Bubbles
• New supersymmetric AdS_3 solutions
• N=31 is not IIB
• Supersymmetric wrapped membranes, AdS(2) spaces, and bubbling geometries
• AdS spacetimes from wrapped D3-branes

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