UC Irvine

Flux compactifications of string theory seem to require the presence of a fine-tuned constant in the superpotential. We discuss a scheme where this constant is replaced by a dynamical quantity which we argue to be a 'continuous Chern-Simons term'. In such a scheme, the gaugino condensate generates the hierarchically small scale of supersymmetry breakdown rather than adjusting its size to a constant. A crucial ingredient is the appearance of the hierarchically small quantity exp(-〈X〉) which corresponds to the scale of gaugino condensation. Under rather general circumstances, this leads to a scenario of moduli stabilization, which is endowed with a hierarchy between the mass of the lightest modulus, the gravitino mass and the scale of the soft terms, m modulus ∼ 〈X〉 m3/2 ∼ 〈X〉2 msoft. The 'little hierarchy' 〈X〉 is given by the logarithm of the ratio of the Planck scale and the gravitino mass, 〈X〉 ∼ log(MPl/m3/2) ∼ 4π2. This exhibits a new mediation scheme of supersymmetry breakdown, called mirage mediation. We highlight the special properties of the scheme, and their consequences for phenomenology and cosmology. © 2005 American Institute of Physics.