SUSY breaking in local string/F-theory models

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 similar to nu(-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/nu(3/2) and may be as small as M-P/nu(2). Since the gravitino mass is of order M-3/2 similar to M-P/nu, 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 nu similar to 10(6-7) in string units, which would give a unification scale of order M-GUT similar to M-s nu(1/6) similar to 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.