Stabilising the supersymmetric Standard Model on the Z6′ orientifold

Four stacks of intersecting supersymmetric fractional D6-branes on the Z6′ 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, Kähler moduli and complex-structure moduli, twisted and untwisted, remain unfixed. Further, some of the Yukawa couplings needed to generate 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 Kähler cone. In principle, missing Yukawa couplings may be restored, albeit with a coupling that is suppressed by non-perturbative effects, by the use of Euclidean D2-branes that are point-like in spacetime, i.e. E2-instantons. However, for the models under investigation, we show that this is not possible.