New Einstein-Sasaki Spaces in Five and Higher Dimensions

TL;DR

This paper constructs new classes of Einstein-Sasaki spaces in five and higher dimensions, expanding the landscape of geometries relevant for string theory and the AdS/CFT correspondence.

Contribution

It introduces infinite families of Einstein-Sasaki metrics with specific symmetries and topologies, derived from BPS limits of Kerr-de Sitter black holes, in various odd dimensions.

Findings

New Einstein-Sasaki spaces L^{p,q,r} in five dimensions with cohomogeneity 2.

Higher-dimensional Einstein-Sasaki spaces with U(1)^{n+1} symmetry.

Topologically S^2 x S^3 in five-dimensional cases.

Abstract

We obtain infinite classes of new Einstein-Sasaki metrics on complete and non-singular manifolds. They arise, after Euclideanisation, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces L^{p,q,r} in five dimensions have cohomogeneity 2, and U(1) x U(1) x U(1) isometry group. They are topologically S^2 x S^3. Their AdS/CFT duals will describe quiver theories on the four-dimensional boundary of AdS_5. We also obtain new Einstein-Sasaki spaces of cohomogeneity n in all odd dimensions D=2n+1 \ge 5, with U(1)^{n+1} isometry.