SUSY breaking and moduli stabilization from fluxes in gauged 6D supergravity

We construct the 4D N = 1 supergravity which describes the low-energy limit of 6D supergravity compactified on a sphere with a monopole background à la Salam and Sezgin. This provides a simple setting sharing the main properties of realistic string compactifications such as flat 4D spacetime, chiral fermions and N = 1 supersymmetry as well as Fayet-Iliopoulos terms induced by the Green-Schwarz mechanism. The matter content of the resulting theory is a supersymmetric SO(3) × U(1) gauge model with two chiral multiplets, S and T. The expectation value of T is fixed by the classical potential, and S describes a flat direction to all orders in perturbation theory. We consider possible perturbative corrections to the Kähler potential in inverse powers of Re S and Re T, and find that under certain circumstances, and when taken together with low-energy gaugino condensation, these can lift the degeneracy of the flat direction for Re S. The resulting vacuum breaks supersymmetry at moderately low energies in comparison with the compactification scale, with positive cosmological constant. It is argued that the 6D model might itself be obtained from string compactifications, giving rise to realistic string compactifications on non Ricci flat manifolds. Possible phenomenological and cosmological applications are briefly discussed.