A Realistic Unified Gauge Coupling from the Micro-Landscape of Orbifold GUTs

TL;DR

This paper develops a calculable framework for gauge coupling unification in 5d orbifold GUTs, linking the 4d gauge coupling to model field content and stabilization mechanisms, and identifies models with realistic unification.

Contribution

It provides explicit two-loop effective potential formulas and a stabilization mechanism that predicts the 4d gauge coupling from 5d model parameters and field content.

Findings

Identifies models with realistic gauge coupling unification.

Provides explicit formulas for the radion effective potential.

Proposes mechanisms for uplifting SUSY-breaking vacua.

Abstract

We consider 5-dimensional supersymmetric field theories where supersymmetry is broken by the Scherk-Schwarz mechanism (or, equivalently, by the F-term VEV of the radion). In such models, the radion effective potential is calculable in terms of the 5d gauge coupling, the UV cutoff of the 5d field theory, and the field content. We provide simple, explicit formulae for the leading part of the two-loop effective potential. Our analysis applies in particular to 5d orbifold GUTs motivated by heterotic orbifold models. We focus on potentially realistic models of this type and make the additional assumption that the UV cutoff scale is identical with the strong-coupling scale of the 5d gauge theory. Given our stabilization mechanism, the 5d radius is now fixed in terms of the 5d gauge coupling and the field content of the model. This implies a prediction for the effective 4d gauge coupling only in terms of the field content of the model. Given the `micro-landscape' provided by the different possible distributions of Standard Model fields between bulk and branes, we find a subset of models with a realistic unified gauge coupling. We also discuss two possibilities for the `uplifting' of our SUSY-breaking AdS vacua: One is based on the possible presence of a weak warping, the other appeals to F-terms in an extra brane-localized SUSY-breaking sector.