ar X iv : 0 90 6 . 45 17 v 2 [ he p - th ] 2 6 Ju n 20 09 Swiss Cheese D 3 - D 7 Soft SUSY Breaking - Revelations

We address issues related to (i) a proposal for resolving a long-standing tension between large volume cosmology and phenomenology as regards reconciliation of requirements of different gravitino masses within the same string-theoretic framework, as well as (ii) evaluation of soft supersymmetry breaking terms and open-string moduli masses in the context of type IIB large volume compactifications involving orientifolds of the Swiss-Cheese Calabi-Yau WCP[1, 1, 1, 6, 9] with a single mobile space-time filling D3brane and stacks of D7-branes wrapping the “big” divisor ΣB as well as supporting D7-brane fluxes. In addition, we also include perturbative α-corrections and non-perturbative world-sheet instanton corrections to the Kähler potential as well as Euclidean D3-instanton superpotential. First, using the toric data for the aforementioned Swiss-Cheese Calabi-Yau and GLSM techniques, we obtain in the large volume limit, the geometric Kähler potential for the big (and small) divisor(s) in terms of derivatives of genustwo Siegel theta functions. Next, we show that as the mobile space-time filling D3-brane moves from a particular non-singular elliptic curve embedded in the Swiss-Cheese Calabi-Yau to another non-singular elliptic curve, it is possible to obtain 10GeV gravitino during the primordial inflationary era as well as, e.g., a TeV gravitino in the present era, within the same set up for the same volume of the Calabi-Yau stabilized at around 10l s . Then by constructing local (i.e. localized around the location of the mobile D3-brane in the Calabi-Yau) appropriate involutively-odd harmonic one-form on the big divisor that lies