Eight-Dimensional Self-Dual Spaces

TL;DR

This paper explores higher-dimensional gravitational instantons by solving self-duality equations in eight dimensions, revealing a non-compact elliptically-fibered self-dual space with Spin(7) holonomy.

Contribution

It introduces a new non-compact solution to the self-duality equations in eight dimensions with elliptic fibration, expanding understanding of special holonomy spaces.

Findings

Found a non-compact elliptically-fibered self-dual space in eight dimensions.

Demonstrated the existence of solutions with Spin(7) holonomy.

Linked self-duality equations to higher-dimensional gravitational instantons.

Abstract

We discuss higher-dimensional gravitational instantons by studying appropriate self-duality equations for the spin connection. In seven and in eight dimensions, the corresponding spaces admit a covariantly constant spinor and have holonomies in G_2 and Spin(7), respectively. We find a non-compact solution to the self-duality equations in eight dimensions in which the self-dual space has an elliptically-fibered structure.