Swiss Cheese D3-D7 Soft SUSY Breaking

TL;DR

This paper explores the geometric and phenomenological aspects of Swiss-Cheese Calabi-Yau compactifications with D3 and D7-branes, deriving moduli-dependent potentials, mass hierarchies, and supersymmetry breaking features relevant for string phenomenology.

Contribution

It introduces a detailed geometric framework for D3-D7 systems in Swiss-Cheese Calabi-Yau compactifications, including new calculations of Kähler potentials, mass spectra, and supersymmetry breaking effects.

Findings

Achieved a geometric Kaehler potential in terms of genus-two Siegel theta functions.

Demonstrated the possibility of obtaining gravitino masses suitable for inflation and present era.

Derived mass hierarchies and universality conditions for moduli and matter fields.

Abstract

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.