Abstract
We analyse type IIA Calabi-Yau orientifolds with background fluxes and D6-branes. The presence of D6-brane deformation moduli redefines the 4d dilaton and complex structure fields and complicates the analysis of such vacua in terms of the effective Kähler potential and superpotential. One may however formulate the F-term scalar potential as a bilinear form on the flux-axion polynomials ρA invariant under the discrete shift symmetries of the 4d effective theory. We express the conditions for Minkoswki and AdS flux vacua in terms of such polynomials, which allow to extend the analysis to include vacua with mobile D6-branes. We find a new, more general class of mathcal{N}=0 Minkowski vacua, which nevertheless present a fairly simple structure of (contravariant) F-terms. We compute the soft-term spectrum for chiral models of intersecting D6-branes in such vacua, finding a quite universal pattern.
Highlights
Needless to say, when combining both ingredients in a single compactification one must do it consistently
A first manifestation of broken supersymmetry are the non-vanishing F-terms in the complex structure moduli sector, yet the genuinely physical observables resulting from spontaneous supersymmetry-breaking correspond to the gravitino mass and soft terms for the visible sector
We compute the gravitino mass and soft terms for the complex structure dominated (CSD) vacua in terms of the axion polynomials of the compactification, in such a way that the vacuum constraints on the axion polynomials suffice to determine whether supersymmetry is broken and how the soft terms relate to the gravitino mass
Summary
Only those small deformations of the D6-brane that respect the SLag conditions with respect to this background have to be considered Even in this approach, the reduction of the tendimensional theory induces kinetic mixing between open string and bulk moduli, such that a redefinition of the complex structure moduli is necessary to identify the proper N = 1 chiral superfields. The function GQ(nk, uΛ) hidden in the Kahler potential (2.9), as inherited from the N = 2 Calabi-Yau compactifications, remains a homogeneous function of degree two in the geometric moduli, but has to be rewritten in terms of the redefined complex structure moduli and the open string moduli: KQ = −2 log GQ nK + 1 ta 2. Where the indices A and B sum over all closed and open string moduli, in line with the conventions used in appendix A to express some revelant properties of the full Kahler potential
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