Sasakian Geometry, Holonomy, and Supersymmetry

Abstract

In this expository article we discuss the relations between Sasakian geometry, reduced holonomy and supersymmetry. It is well known that the Riemannian manifolds other than the round spheres that admit real Killing spinors are precisely Sasaki-Einstein manifolds, 7-manifolds with a nearly parallel G2 structure, and nearly Kaehler 6-manifolds. We then discuss the relations between the latter two and Sasaki-Einstein geometry.

40 pages, some minor corrections made, to appear in the Handbook of pseudo-Riemannian Geometry and Supersymmetry

References in corpus (19)

• The Anthropic Landscape of String Theory
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• New Einstein-Sasaki Spaces in Five and Higher Dimensions
• Toric Sasaki-Einstein metrics on S^2 x S^3
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• Cohomogeneity One Manifolds of Spin(7) and G(2) Holonomy
• Supersymmetry breaking at the end of a cascade of Seiberg dualities
• A New Infinite Class of Quiver Gauge Theories
• Kaehler reduction of metrics with holonomy G_2
• Scalar Laplacian on Sasaki-Einstein Manifolds Y^{p,q}
• On Spin(7) holonomy metric based on SU(3)/U(1): II
• Matter From G(2) Manifolds
• Explicit Toric Metric on Resolved Calabi-Yau Cone
• Sasaki-Einstein Twist of Kerr-AdS Black Holes
• On Stable Non-Supersymmetric Vacua at the Bottom of Cascading Theories
• Parallel spinors and holonomy groups
• Compact weak G_2-manifolds with conical singularities
• A new Ricci flat geometry
• Supersymmetric solutions based on Y^{p,q} and L^{p,q,r}

Cited by in corpus (12)

• Killing-Yano tensors and some applications
• Instantons on Special Holonomy Manifolds
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
• Instantons on sine-cones over Sasakian manifolds
• A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
• A new $\frac{1}{2}$-Ricci type formula on the spinor bundle and applications
• On the Holonomy of Kaluza-Klein metrics
• Topological Vertex, String Amplitudes and Spectral Functions of Hyperbolic Geometry
• Toric data and Killing forms on homogeneous Sasaki-Einstein manifold $T^{1,1}$
• Families of solutions of the heterotic G${}_2$ system
• Vector bundles on Sasakian manifolds