Swiss Cheese D3-D7 Soft SUSY Breaking

In type IIB large volume compactifications involving orientifolds of the Swiss-Cheese Calabi-Yau [11169] with a single mobile space-time filling D3-brane and stacks of D7-branes wrapping the "big" divisor (D_5) and supporting D7-brane fluxes, (i) using the toric data and GLSM techniques, we obtain the geometric Kaehler potential for D_5 in terms of genus-two Siegel theta functions; (ii) we show that as the D3-brane moves from a particular embedded non-singular elliptic curve to another one, it is possible to obtain 10^{12}GeV gravitino during the inflationary era as well as a TeV gravitino in the present era, for the same vol(CY)~10^6l_s^6; (iii) by constructing local appropriate involutively-odd harmonic one-form on D_5 that lies in the cokernel of the pullback of the immersion map, we show that it is possible to obtain an O(1) g_{YM} from the wrapping of D7-branes on D_5 due to competing contributions from the Wilson line moduli relative to the divisor volume modulus (to permit gaugino condensation [gc], we consistently consider zero sections of ND_5) - to simplify we restrict the D3-brane to D_5 which means W_gc=0; (iv) we obtain gaugino masses of the order of gravitino mass and the matter fields' masses to be enhanced relative to the gravitino mass; (v) the anomaly-mediated gaugino masses are found to be suppressed relative to the gravity-mediated gaugino masses by the standard loop factor; (vi) new sub-dominant mu-terms are obtained from section of the (small) divisor bundle encoding information about the ED3- instanton fluctuation determinant; (vii) we obtain a (near)universality in the masses, hat(mu), hat(Y) and the hat(mu)B-terms for the D3 position moduli and a hierarchy in the same set and a universality in the A-terms on inclusion of D7 Wilson line moduli.

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