Octonionic Gravitational Instantons

TL;DR

This paper constructs eight-dimensional gravitational instantons with $Spin(7)$ holonomy, explores their topological properties, and lifts them to string and M-theory configurations preserving supersymmetry.

Contribution

It introduces a new class of eight-dimensional gravitational instantons with $Spin(7)$ holonomy and extends these solutions to higher-dimensional string and M-theory backgrounds.

Findings

Constructed $Spin(7)$ holonomy gravitational instanton with S^4 bolt

Identified boundary at infinity as squashed S^7

Lifted solutions to string and M-theory preserving 1/16 supersymmetry

Abstract

We construct eight-dimensional gravitational instantons by solving appropriate self-duality equations for the spin-connection. The particular gravitational instanton we present has $Spin(7)$ holonomy and, in a sense, it is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a removable bolt singularity which is topologically S^4 and its boundary at infinity is the squashed S^7. We also lift our solutions to ten and eleven dimensions and construct fundamental string and membrane configurations that preserve 1/16 of the original supersymmetries.