Gauge-top unification

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Higher-dimensional models of grand unification allow us to relate the top Yukawa coupling yₜ to the gauge coupling g. The tree level relation yₜ=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, yₜ 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.