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

TL;DR

This paper investigates the geometry and topology of two infinite families of toric Sasaki-Einstein seven-manifolds, Y^{p,k}, which are relevant for AdS_4/CFT_3 dualities involving N=2 superconformal field theories.

Contribution

It provides explicit descriptions of the Y^{p,k} manifolds, including their toric diagrams and gauged linear sigma model charges, and explores their interpolation between known homogeneous spaces.

Findings

Y^{p,k} manifolds are Lens space bundles over CP^2 and CP^1 x CP^1.

They interpolate between orbifolds of S^7, M^{3,2}, and Q^{1,1,1}.

The Calabi-Yau cones are toric and explicitly characterized.

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}.