Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold

We study the effects of adding RR, NS and metric fluxes on a T^6/(\Omega(-1)^{F_L} I_3) Type IIA orientifold. By using the effective flux-inducedsuperpotential we obtain Minkowski or AdS vacua with broken or unbrokensupersymmetry. In the Minkowski case some combinations of real moduli remainundetermined, whereas all can be stabilized in the AdS solutions. Many fluxparameters are available which are unconstrained by RR tadpole cancellationconditions allowing to locate the minima at large volume and small dilaton. Wealso find that in AdS supersymmetric vacua with metric fluxes, the overall fluxcontribution to RR tadpoles can vanish or have opposite sign to that ofD6-branes, allowing for new model-building possibilities. In particular, weconstruct the first N=1 supersymmetric intersecting D6-brane models withMSSM-like spectrum and with all closed string moduli stabilized. Someaxion-like fields remain undetermined but they are precisely required to giveSt\"uckelberg masses to (potentially anomalous) U(1) brane fields. We show thatthe cancellation of the Freed-Witten anomaly guarantees that the axions withflux-induced masses are orthogonal to those giving masses to the U(1)'s.Cancellation of such anomalies also guarantees that the D6-branes in our N=1supersymmetric AdS vacua are calibrated so that they are forced to preserve oneunbroken supersymmetry.Comment: 61 pages, Latex, v2: added references, v3: minor correction