Supersymmetric Domain Walls from Metrics of Special Holonomy

TL;DR

This paper introduces new supersymmetric domain-wall metrics derived from special holonomy spaces via a Heisenberg limit, with potential applications in resolving singularities and holography.

Contribution

It presents a novel method to obtain supersymmetric domain-wall metrics from known special holonomy metrics through a Heisenberg limit, expanding the toolkit for holography and singularity resolution.

Findings

Metrics admit generalized Heisenberg isometry groups

Explicit metrics suggest broad applicability

New inhomogeneous metrics of special holonomy provided

Abstract

Supersymmetric domain-wall spacetimes that lift to Ricci-flat solutions of M-theory admit generalized Heisenberg (2-step nilpotent) isometry groups. These metrics may be obtained from known cohomogeneity one metrics of special holonomy by taking a "Heisenberg limit", based on an In\"on\"u-Wigner contraction of the isometry group. Associated with each such metric is an Einstein metric with negative cosmological constant on a solvable group manifold. We discuss the relevance of our metrics to the resolution of singularities in domain-wall spacetimes and some applications to holography. The extremely simple forms of the explicit metrics suggest that they will be useful for many other applications. We also give new but incomplete inhomogeneous metrics of holonomy SU(3), $G_2$ and Spin(7), which are $T_1$, $T_2$ and $T_3$ bundles respectively over hyper-K\"ahler four-manifolds.