Gauge-top unification

TL;DR

This paper explores how higher-dimensional grand unification models relate the top Yukawa coupling to gauge coupling, showing that localized Fayet-Iliopoulos terms and compactification geometry influence tan beta predictions.

Contribution

It demonstrates that localized Fayet-Iliopoulos terms suppress y_t relative to g, linking tan beta to the geometry of compact space in orbifold GUT models.

Findings

Y_t=g at GUT scale implies small tan beta without corrections.

Localized Fayet-Iliopoulos terms increase tan beta predictions.

Anisotropic orbifold compactifications are favored for realistic models.

Abstract

Higher-dimensional models of grand unification allow us to relate the top Yukawa coupling y_t to the gauge coupling g. The tree level relation y_t=g at the scale of grand unification implies, in the framework of the MSSM, a rather small ratio of Higgs expectation values tan beta. We find that, in the presence of localized Fayet-Iliopoulos terms, y_t is suppressed against g because the bulk fields acquire non-trivial profiles whose overlap is smaller than in the case of flat profiles. This increases the prediction for tan beta to moderately large values. Thus tan beta is related to the geometry of compact space. We also discuss explicit realizations of such settings in orbifold compactifications of the heterotic string. It turns out that anisotropic compactifications, allowing for an orbifold GUT interpretation, are favored.