Explaining the Electroweak Scale and Stabilizing Moduli in M Theory

TL;DR

This paper elaborates on how M theory vacua stabilize moduli and generate a stable hierarchy, predicts suppressed gaugino masses, and suggests gravitino masses naturally fall within the TeV to 100 TeV range.

Contribution

It provides a detailed explanation and generalization of previous results on moduli stabilization in M theory, identifying a nearly unique de Sitter vacuum with phenomenological implications.

Findings

Gaugino masses are significantly suppressed relative to the gravitino mass.

Small vacuum energy vacua have gravitino masses in the TeV to 100 TeV range.

A nearly unique de Sitter vacuum is identified under reasonable conditions.

Abstract

In a recent paper \cite{Acharya:2006ia} it was shown that in $M$ theory vacua without fluxes, all moduli are stabilized by the effective potential and a stable hierarchy is generated, consistent with standard gauge unification. This paper explains the results of \cite{Acharya:2006ia} in more detail and generalizes them, finding an essentially unique de Sitter (dS) vacuum under reasonable conditions. One of the main phenomenological consequences is a prediction which emerges from this entire class of vacua: namely gaugino masses are significantly suppressed relative to the gravitino mass. We also present evidence that, for those vacua in which the vacuum energy is small, the gravitino mass, which sets all the superpartner masses, is automatically in the TeV - 100 TeV range.