A Moduli Fixing Mechanism in M theory

TL;DR

This paper explores how fluxes and singularities in M theory compactifications on G2-manifolds can stabilize moduli, potentially explaining the hierarchy problem with a supersymmetric AdS vacuum.

Contribution

It demonstrates a mechanism for moduli stabilization in M theory using fluxes and singularities, leading to an isolated supersymmetric minimum with a negative cosmological constant.

Findings

Moduli can be stabilized with an isolated supersymmetric minimum.

The fundamental scale can be around 10 TeV, addressing the hierarchy problem.

Hyperbolic three-manifolds play a role in the topological aspects.

Abstract

We study M theory compactifications on manifolds of $G_2$-holonomy with gauge and matter fields supported at singularities. We show that, under certain topological conditions, the combination of background $G$-flux and background fields at the singularities induces a potential for the moduli with an isolated minimum. The theory in the minimum is supersymmetric and has a negative cosmological constant in the simplest case. In a more realistic scenario, we find that the fundamental scale is around 10 Tev and the heirarchy between the four dimensional Planck and electroweak scales may be explained by the value of a topological invariant. Hyperbolic three-manifolds enter the discussion in an interesting way.