Stabilising the supersymmetric Standard Model on the Z_6' orientifold

Four stacks of intersecting supersymmetric fractional D6-branes on the Z_6' orientifold have previously been used to construct consistent models having the spectrum of the supersymmetric Standard Model, including a single pair of Higgs doublets, plus three right-chiral neutrino singlets. However, various moduli, Kahler moduli and complex-structure moduli, twisted and untwisted, remain unfixed. Further, some of the Yukawa couplings needed to generated quark and lepton masses are forbidden by a residual global symmetry of the model. In this paper we study the stabilisation of moduli using background fluxes, and show that the moduli may be stabilised within the Kahler cone. In principle, missing Yukawa couplings may be restored, albeit with a coupling that is suppressed by non-perturbative effects, by the use Euclidean D2-branes that are pointlike in spacetime, i.e. E2-instantons. However, for the models under investigation, we show that this is not possible.