Towards a theory of quark masses, mixings and CP-violation

We discuss the structure of Yukawa couplings in D-brane models in which the SM fermion spectrum appears at the intersections of D-branes wrapping a compact space. In simple toroidal realistic examples one can explicitly compute the Yukawa couplings as a function of the geometrical data summing over world-sheet instanton contributions. A particular simple model with a N = 1 SUSY spectrum and three quark-lepton generations is studied in some detail. Remarkably, one can reproduce the observed spectrum of quark masses and mixings for particular choices of the compact radii and brane locations. In order to reproduce the smallness of upand down-quark masses branes should be located in simple geometric configurations leading to some accidental global symmetries. We also find that the brane configurations able to reproduce the observed data may be considered as a deformation (by brane translation) of a configuration with Pati-Salam gauge symmetry. The origin of CP-violation in this formalism is quite elegant. It appears as a consequence of the generic presence of U(1) Wilson line backgrounds in the compact dimensions. One can reproduce the observed results for the CP-violation Jarlskog invariant J as long as the compact radii are of order of the string scale.