Notes on toric Sasaki-Einstein seven-manifolds and AdS_4/CFT_3

Abstract

We study the geometry and topology of two infinite families Y^{p,k} of Sasaki-Einstein seven-manifolds, that are expected to be AdS_4/CFT_3 dual to families of N=2 superconformal field theories in three dimensions. These manifolds, labelled by two positive integers p and k, are Lens space bundles S^3/Z_p over CP^2 and CP^1 x CP^1, respectively. The corresponding Calabi-Yau cones are toric. We present their toric diagrams and gauged linear sigma model charges in terms of p and k, and find that the Y^{p,k} manifolds interpolate between certain orbifolds of the homogeneous spaces S^7, M^{3,2} and Q^{1,1,1}.

31 pages, 6 toric figures; v2: minor changes

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• Symmetry-breaking vacua and baryon condensates in AdS/CFT
• Superconformal field theories from crystal lattices
• Supersymmetric AdS Backgrounds in String and M-theory
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• Lectures on Generalized Complex Geometry for Physicists
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• (Un)Higgsing the M2-brane
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• Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory
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• New Gauged Linear Sigma Models for 8D HyperKahler Manifolds and Calabi-Yau Crystals
• The AdS/CFT Correspondence and Symmetry Breaking
• Semiclassics of three-dimensional SCFTs from holography