M-theory on seven-dimensional manifolds with SU(3) structure

TL;DR

This paper explores M-theory compactifications on seven-dimensional manifolds with SU(3) structure, deriving effective theories with varying supersymmetry and demonstrating moduli stabilization without non-perturbative effects.

Contribution

It provides a detailed analysis of M-theory on SU(3) structured manifolds, including the gravitino mass matrix and explicit examples of moduli stabilization.

Findings

Vacua with no, N=2, or N=1 supersymmetry identified

Explicit moduli stabilization achieved without non-perturbative effects

Effective N=1 theory derived for specific internal manifolds

Abstract

In this paper we study M-theory compactifications on seven-dimensional manifolds with SU(3) structure. As such manifolds naturally pick out a specific direction, the resulting effective theory can be cast into a form which is similar to type IIA compactifications to four dimensions. We derive the gravitino mass matrix in four dimensions and show that for different internal manifolds (torsion classes) the vacuum preserves either no supersymmetry, or N=2 supersymmetry or, through spontaneous partial supersymmetry breaking, N=1 supersymmetry. For the latter case we derive the effective N=1 theory and give explicit examples where all the moduli are stabilised without the need of non-perturbative effects.