A New Construction of Einstein-Sasaki Metrics in D >= 7

TL;DR

This paper introduces explicit Einstein-Kahler and Einstein-Sasaki metrics in higher dimensions, including a NUT parameter, with potential applications in M-theory and the AdS/CFT correspondence.

Contribution

It presents a new construction method for Einstein-Kahler and Einstein-Sasaki metrics in all even and odd dimensions with additional parameters, expanding the class of known solutions.

Findings

Explicit Einstein-Kahler metrics in dimensions ≥6 with NUT parameter.

Construction of Einstein-Sasaki metrics in dimensions ≥7 from these Einstein-Kahler metrics.

Examples of smooth, complete Einstein-Sasaki spaces in seven dimensions.

Abstract

We construct explicit Einstein-Kahler metrics in all even dimensions D=2n+4 \ge 6, in terms of a $2n$-dimensional Einstein-Kahler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, in addition to mass and rotation parameters. Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5 \ge 7. As is commonly the case in this type of construction, for suitable choices of the free parameters the Einstein-Sasaki metrics can extend smoothly onto complete and non-singular manifolds, even though the underlying Einstein-Kahler metric has conical singularities. We discuss some explicit examples in the case of seven-dimensional Einstein-Sasaki spaces. These new spaces can provide supersymmetric backgrounds in M-theory, which play a role in the AdS_4/CFT_3 correspondence.