A Note on Compactifications on Spin(7)-Holonomy Manifolds

TL;DR

This paper investigates M-theory compactifications on Spin(7)-holonomy manifolds with warp factors, deriving conditions for unbroken supersymmetry and equations for the 4-form field strength.

Contribution

It provides new equations relating the 4-form field strength, warp factor, and Spin(7) structure in M-theory compactifications.

Findings

Derived conditions for unbroken N=1 supersymmetry.

Established relations between 4-form field strength and warp factor.

Analyzed implications for three-dimensional Minkowski vacua.

Abstract

In this note we consider compactifications of ${\cal M}$-theory on $Spin(7)$-holonomy manifolds to three-dimensional Minkowski space. In these compactifications a warp factor is included. The conditions for unbroken N=1 supersymmetry give rise to determining equations for the 4-form field strength in terms of the warp factor and the self-dual 4-form of the internal manifold.