Sasaki-Einstein Metrics on S^2 x S^3

TL;DR

The paper constructs a countable family of co-homogeneity one Sasaki-Einstein metrics on $S^2\times S^3$, including both quasi-regular and irregular cases, and shows they yield AdS5 backgrounds whose dual 4D ${\cal N}=1$ SCFTs exhibit either rational or irrational central charges depending on regularity. The authors formulate these spaces as $S^1$ bundles $Y^{p,q}$ over $S^2\times S^2$, derive global regularity conditions, and classify the resulting metrics via the parameters $(p,q)$ and $a$, yielding infinite families with explicit geometric and topological data. They present a canonical Sasaki-Einstein form, analyze global Sasaki structures, and discuss special limits reproducing known spaces like $T^{1,1}$ and $S^5/\mathbb{Z}_2$, as well as dual field theory implications, including R-symmetry and central charges. Overall, the work expands the landscape of explicit Sasaki-Einstein manifolds and clarifies how geometric regularity correlates with properties of the dual SCFTs.

Abstract

We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S^2 x S^3, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected to be dual to N=1 superconformal field theories in four-dimensions with compact or non-compact R-symmetry and rational or irrational central charges, respectively.