SUSY Breaking in Local String/F-Theory Models

Abstract

We investigate bulk moduli stabilisation and supersymmetry breaking in local string/F-theory models where the Standard Model is supported on a del Pezzo surface or singularity. Computing the gravity mediated soft terms on the Standard Model brane induced by bulk supersymmetry breaking in the LARGE volume scenario, we explicitly find suppressions by M_s/M_P ~ V^{-1/2} compared to M_{3/2}. This gives rise to several phenomenological scenarios, depending on the strength of perturbative corrections to the effective action and the source of de Sitter lifting, in which the soft terms are suppressed by at least M_P/V^{3/2} and may be as small as M_P/V^2. Since the gravitino mass is of order M_{3/2} ~ M_P/V, for TeV soft terms all these scenarios give a very heavy gravitino (M_{3/2} >= 10^8 GeV) and generically the lightest moduli field is also heavy enough (m >= 10 TeV) to avoid the cosmological moduli problem. For TeV soft terms, these scenarios predict a minimal value of the volume to be V ~ 10^{6-7} in string units, which would give a unification scale of order M_{GUT} ~ M_s V^{1/6} ~ 10^{16} GeV. The strong suppression of gravity mediated soft terms could also possibly allow a scenario of dominant gauge mediation in the visible sector but with a very heavy gravitino M_{3/2} > 1 TeV.