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 T6/(Ω(-1)FLI3) type IIA orientifold. By using the effective flux-induced superpotential we obtain Minkowski or AdS vacua with broken or unbroken supersymmetry. In the Minkowski case some combinations of real moduli remain undetermined, whereas all can be stabilized in the AdS solutions. Many flux parameters are available which are unconstrained by RR tadpole cancellation conditions allowing to locate the minima at large volume and small dilaton. We also find that in AdS supersymmetric vacua with metric fluxes, the overall flux contribution to RR tadpoles can vanish or have opposite sign to that of D6-branes, allowing for new model-building possibilities. In particular, we construct the first N = 1 supersymmetric intersecting D6-brane models with MSSM-like spectrum and with all closed string moduli stabilized. Some axion-like fields remain undetermined but they are precisely required to give Stueckelberg masses to (potentially anomalous) U(1) brane fields. We show that the cancellation of the Freed-Witten anomaly guarantees that the axions with flux-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 = 1 supersymmetric AdS vacua are calibrated so that they are forced to preserve one unbroken supersymmetry