Dynamical gauge coupling unification from moduli stabilization

In D-brane models, different part of the 4-dimensional gauge group might originate from D-branes wrapping different cycles in the internal space, and then the standard model gauge couplings at the compactification scale are determined by different cycle-volume moduli. We point out that those cycle-volume moduli can naturally have universal vacuum expectation values up to small deviations suppressed by 1/8π2 if they are stabilized by KKLT-type non-perturbative superpotential with properly chosen discrete parameters. This dynamical unification of gauge couplings is independent of the detailed form of the moduli Kähler potential, but relies crucially on the existence of low energy supersymmetry. If supersymmetry is broken by an uplifting brane as in KKLT compactification, again independently of the detailed form of the moduli Kähler potential, the moduli-mediated gaugino masses at the compactification scale are universal also, and are comparable to the anomaly-mediated gaugino masses. As a result, both the gauge coupling unification at high energy scale and the mirage mediation pattern of soft supersymmetry breaking masses are achieved naturally even when the different sets of the standard model gauge bosons originate from D-branes wrapping different cycles in the internal space.