Gluino Condensation in Strongly Coupled Heterotic String Theory

TL;DR

This paper investigates gluino condensation in strongly coupled heterotic string theory compactified on a Calabi-Yau manifold, proposing a novel supersymmetry breaking mechanism influenced by the orbifold topology, with implications for hierarchy and cosmological constant.

Contribution

It introduces a new perspective on supersymmetry breaking via gluino condensation in M-theory, emphasizing the role of orbifold topology and Casimir-like effects.

Findings

Supersymmetry can remain locally unbroken despite gluino condensation.

Global topology of the orbifold causes supersymmetry breaking.

The mechanism suggests a natural hierarchy of scales and insights into moduli stabilization.

Abstract

Strongly coupled heterotic $E_8\times E_8$ string theory, compactified to four dimensions on a large Calabi-Yau manifold ${\bf X}$, may represent a viable candidate for the description of low-energy particle phenomenology. In this regime, heterotic string theory is adequately described by low-energy $M$-theory on ${\bf R}^4\times{\bf S}^1/{\bf Z}_2\times{\bf X}$, with the two $E_8$'s supported at the two boundaries of the world. In this paper we study the effects of gluino condensation, as a mechanism for supersymmetry breaking in this $M$-theory regime. We show that when a gluino condensate forms in $M$-theory, the conditions for unbroken supersymmetry can still be satisfied locally in the orbifold dimension ${\bf S}^1/{\bf Z}_2$. Supersymmetry is then only broken by the global topology of the orbifold dimension, in a mechanism similar to the Casimir effect. This mechanism leads to a natural hierarchy of scales, and elucidates some aspects of heterotic string theory that might be relevant to the stabilization of moduli and the smallness of the cosmological constant.