Swiss-cheese D3– D7 soft SUSY breaking

Abstract

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 4 [ 1 , 1 , 1 , 6 , 9 ] with a single mobile space–time filling D3-brane and stacks of D7-branes wrapping the “big” divisor Σ B 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 genus-two 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 10 12 GeV 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 10 6 l s 6 . 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 in coker ( H ∂ ¯ , − ( 0 , 1 ) ( CY 3 ) → i ∗ H ∂ ¯ , − ( 0 , 1 ) ( Σ B ) ) and extremizing the potential, we show that it is possible to obtain an O ( 1 ) g YM from the wrapping of D7-branes on the big divisor due to competing contributions from the Wilson line moduli relative to the divisor volume modulus. To permit gaugino condensation, we take the rigid limit of the big divisor by considering zero sections of the normal bundle of the same – the same being justified by the extremization of the potential. For the purposes of calculation of the gaugino masses, matter moduli masses and soft supersymmetry breaking parameters, we restrict the mobile D3-brane to the big divisor – this has the additional advantage of nullification of the superpotential generated from gaugino condensation. With the inclusion of the matter moduli corresponding to the position moduli of the mobile D3-brane and the Wilson line moduli corresponding to the D7-branes, we obtain gaugino masses of the order of gravitino mass and the matter fields' masses to be enhanced relative to the gravitino mass. The anomaly-mediated gaugino masses are found to be suppressed relative to the gravity-mediated gaugino masses by the standard loop factor. New non-zero contributions to the μ-terms, though sub-dominant in the large volume limit, are obtained from section of the (small) divisor bundle encoding information about the ED3-instanton fluctuation determinant, filling D3-brane and the Wilson line moduli. There is a (near) universality in the masses, μ ˆ -parameters, Yukawa couplings and the μ ˆ B -terms for the D3-brane position moduli – the Higgs doublet in our construction – and a hierarchy in the same set and a universality in the A-terms on inclusion of the D7-brane Wilson line moduli.