Spin(7)-manifolds with three-torus symmetry

TL;DR

This paper characterizes Spin(7)-holonomy manifolds with three-torus symmetry using tri-symplectic geometry, expanding the understanding of such manifolds beyond supergravity applications.

Contribution

It introduces a new description of Spin(7)-holonomy manifolds with three-torus symmetry via tri-symplectic geometry of four-manifolds.

Findings

Provides a geometric framework for Spin(7) manifolds with symmetry

Connects exceptional holonomy metrics to tri-symplectic structures

Extends examples beyond supergravity contexts

Abstract

Metrics of exceptional holonomy are vacuum solutions to the Einstein equation. In this paper we describe manifolds with holonomy contained in Spin(7) preserved by a three-torus symmetry in terms of tri-symplectic geometry of four-manifolds. These complement examples that have appeared in the context of domain wall problems in supergravity.