Moduli Stabilization in Heterotic $M$-theory

TL;DR

This paper investigates how to stabilize key moduli in heterotic M-theory using gaugino condensations and membrane instantons, aiming to achieve realistic vacuum expectations for the length of the eleventh dimension and the internal volume.

Contribution

It demonstrates a mechanism for moduli stabilization in heterotic M-theory through combined effects of gaugino condensations and membrane instantons.

Findings

Vacuum expectation values of moduli can be phenomenologically favored.

Multi-gaugino condensations and membrane instantons are effective in stabilization.

Conditions for stabilization are explicitly identified.

Abstract

We examine the stabilization of the two typical moduli, the length $\rho$ of the eleventh segment and the volume $V$ of the internal six manifold, in compactified heterotic $M$-theory. It is shown that, under certain conditions, the phenomenologically favored vacuum expectation values of $\rho$ and $V$ can be obtained by the combined effects of multi-gaugino condensations on the hidden wall and the membrane instantons wrapping the three cycle of the internal six manifold.