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 nonsingular elliptic curve, it is possible to obtain 10 12 GeV gravitino during the primordial inflationary era as well as, e.g., a T eV gravitino in the present era, within the same set up for the same volume of the Calabi-Yau stabilized at around 10 6 l (Σ B ) and extremizing the potential, we show that it is possible to obtain an O(1) g Y M 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-parameters, Yukawa couplings and theμB-terms for the D3-brane position moduli -the Higgs doublet in our constr...

"Big" Divisor D3/D7 Swiss-Cheese Phenomenology

“…As was shown in [24], the following basis of fluctuations simultaneously diagonalizesK ij and Z ij :…”

“…The main idea of our proposal [24] pertaining to the geometric resolution of the tension between LVS cosmology and phenomenology, is the motion of a space-time filling mobile D3-brane which dictates the gravitino mass via a holomorphic pre-factor in the superpotential -section of (the appropriate) divisor bundle. The gravitino mass is given by:…”

“…Taking the small divisor's volume modulus and the Calabi-Yau volume modulus as independent variables, one can show that the volume of the Calabi-Yau can be extremized at one value -10 6 -for varying positions of the mobile D3-brane (See [24]). Apart from details given in [24], some of the major contributory reasons include (a) the D3-brane position moduli enter the Calabi-Yau volume-independent holomorphic prefactor in the superpotential and hence the extremization of the overall potential (proportional to the modulus squared of the prefactor) with respect to the volume modulus, is not influenced by this prefactor, and (b) in consistently taking the large volume limit as done in this paper, the superpotential is independent of the Calabi-Yau volume modulus.…”

“…where σ S (and for later uses, σ B ) is the volume of the small (big) divisor complexified by the RR four-form axion, the constants λ 1,2 are functions of the extremum values of the closed string moduli and the FayetIlliopoulos parameters corresponding to the NLSM (the IR limit of the GLSM) for an underlying N = 2 supersymmetric gauge theory whose target space is the (toric) projective variety we are considering in our work, and the mobile D3-brane position moduli fluctuations δZ i 's and the D7−brane Wilson line moduli fluctuations δà I 's (I indexes dim H (0,1) ∂,− (CY 3 ) and for simplicity we take I = 1 corresponding to the harmonic one-form referred to earlier on in this section and explicitly constructed in [24]), obtained in [24], diagonalize the open string moduli metric.…”

“…Using GLSM techniques and the toric data for the given Swiss-Cheese Calabi-Yau, the geometric Kähler potential for the divisor Σ B (and Σ S ) in the LVS limit was evaluated in [24] in terms of derivatives of genus-two Siegel theta functions as well as two Fayet-Iliopoulos parameters corresponding to the two C * actions in the two-dimensional N = 2 supersymmetric gauge theory whose target space is our toric variety Calabi-Yau, and a parameter ζ encoding the information about the D3−brane position moduli-independent (in the LVS limit) period matrix of the hyperelliptic curve w 2 = P Σ B (z), P Σ B (z) being the defining hypersurface for Σ B . The geometric Kähler potential for the divisor D 5 in the LVS limit is hence given by:…”