Notes on toric Sasaki-Einstein seven-manifolds and AdS4/CFT3

We study the geometry and topology of two infinite families Yp,k of Sasaki-Einstein seven-manifolds, that are expected to be AdS(4)/CFT3 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 CP2 and CP1 x CP1, 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,Y- k manifolds interpolate between certain orbifolds of the homogeneous spaces S-7, M-3,M-2 and Q(1,1,1).