A New Infinite Class of Sasaki-Einstein Manifolds

TL;DR

This paper constructs an infinite class of Sasaki-Einstein manifolds from positive curvature Kähler-Einstein manifolds, leading to new supergravity solutions with potential applications in superconformal field theories.

Contribution

It introduces a novel infinite family of Sasaki-Einstein manifolds associated with any positive curvature Kähler-Einstein manifold, expanding the landscape of supergravity solutions.

Findings

Recover a known family of solutions for n=1

Derive new solutions for n=2

Potential duals for superconformal field theories

Abstract

We show that for every positive curvature Kahler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X_{2n+3} in dimension 2n+3. When n=1 we recover a recently discovered family of supersymmetric AdS_5 x X_5 solutions of type IIB string theory, while when n=2 we obtain new supersymmetric AdS_4 x X_7 solutions of D=11 supergravity. Both are expected to provide new supergravity duals of superconformal field theories.