Soft SUSY breaking parameters and RG running of squark and slepton masses in large volume Swiss Cheese compactifications

We consider type IIB large volume compactifications involving orientifolds of the Swiss Cheese Calabi-Yau WCP4[1,1,1,6,9] with a single mobile space-time filling D3-brane and stacks of D7-branes wrapping the “big” divisor ΣB (as opposed to the “small” divisor usually done in the literature thus far) as well as supporting D7-brane fluxes. After reviewing our proposal of [1] (Misra and Shukla, 2010) for resolving a long-standing tension between large volume cosmology and phenomenology pertaining to obtaining a 1012 GeV gravitino in the inflationary era and a TeV gravitino in the present era, and summarizing our results of [1] (Misra and Shukla, 2010) on soft supersymmetry breaking terms and open-string moduli masses, we discuss the one-loop RG running of the squark and slepton masses in mSUGRA-like models (using the running of the gaugino masses) to the EW scale in the large volume limit. Phenomenological constraints and some of the calculated soft SUSY parameters identify the D7-brane Wilson line moduli as the first two generations/families of squarks and sleptons and the D3-brane (restricted to the big divisor) position moduli as the two Higgses for MSSM-like models at TeV scale. We also discuss how the obtained open-string/matter moduli make it easier to impose FCNC constraints, as well as RG flow of off-diagonal squark mass(-squared) matrix elements.