Grand Unification in Higher Dimensions with Split Supersymmetry

Abstract

We investigate gauge coupling unification in higher dimensional GUT models with split supersymmetry. We focus on 5d and 6d orbifold GUTs, which permit a simple solution to several problems of 4D GUTs as well as control over GUT scale threshold corrections. In orbifold GUTs, calculable threshold corrections can raise or lower the prediction for $\alpha_s(M_Z)$ in a way that depends on the location of Higgs fields. On the other hand, split supersymmetry lowers the prediction for $\alpha_s(M_Z)$. Consequently, split supersymmetry changes the preferred location of the Higgs fields in orbifold GUTs. In the simplest models, we find that gauge coupling unification favors higgs doublets that live on the orbifold fixed points instead of in the bulk. In addition, relatively high scales of supersymmetry breaking of $10^{10\pm 2}$ GeV are generically favored.