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Varying alpha, thresholds and extra dimensions

We consider variations of coupling strengths and mass ratios in and beyond the Standard Model, in the light of various mechanisms of mass generation. In four-dimensional unified models, heavy quark and superparticle thresholds and the electron mass can completely alter the (testable) relation between Delta ln alpha and Delta ln mu, where mu \equiv m_p/m_e. In extra-dimensional models where a compactification scale below the fundamental scale is varying, definite predictions may result even without unification; we examine some models with Scherk-Schwarz supersymmetry-breaking.