Complete gauge threshold corrections for intersecting fractional D6-branes: The Z6 and Z6′ Standard Models

We perform a complete analysis of one-loop threshold corrections to the gauge couplings of fractional D6-branes. This includes besides SU(N) also symplectic, orthogonal and massless Abelian gauge factors and the full computation of contributions from discrete and continuous Wilson lines and brane displacements. Two classes of globally consistent supersymmetric compactifications with Standard Model spectra on T6/Z6 and T6/Z6′ are presented in detail with the latter exhibiting the potential of supersymmetry breaking via a hidden sector gaugino condensate. The T6/Z6′ Standard Models are completely classified, and it turns out that out of 768 distinct D6-brane configurations only 16 different sets of massless spectra and ten distinct values of gauge couplings at one-loop arise. The gauge threshold corrections enhance the diversity to 196 nonequivalent models.