Abstract
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, 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.
Highlights
The attraction of using intersecting D6-branes in a bottom-up approach to constructing the StandardModel is well known [1], and models having just the spectrum of the Standard Model have been constructed [2, 3]
Non-supersymmetric intersecting-brane models lead to flavour-changing neutralcurrent (FCNC) processes induced by stringy instantons that can only be suppressed to levels consistent with current bounds by choosing a high string scale, of order 104 TeV, which in turn leads to fine tuning problems [4]
In previous papers [10, 11, 12] we have studied orientifolds with the point group P = Z′6, and derived models having the spectrum of the supersymmetric Standard Model plus three right-chiral neutrinos
Summary
Model is well known [1], and models having just the spectrum of the Standard Model have been constructed [2, 3]. Running from the string scale to the TeV scale with the three-generation supersymmetric Standard Model spectrum, none of our solutions can reproduce the measured values of the non-abelian coupling strengths of the SU (3)colour and SU (2)L gauge groups. The only supersymmetric models obtained in [10] yielding three chiral generations 3QL of quark doublets via (a∩b, a∩b′) = (2, 1) or (1, 2), having no chiral matter in symmetric representations of the gauge groups, and not too much in antisymmetric representations, that produce non-abelian coupling constant unification, are the two solutions on the BAB lattice given in Table 15 of that paper. The best we can do yields two additional vector-like Higgs doublets 2(Hu + Hd) and four additional vector-like charged lepton singlets 4(lcL + lcL), and in any case the weak hypercharge U (1)Y gauge coupling strength αY = 3α3/5 as required by the “observed” standard-model unification. We investigate the utility of non-perturbative effects, so-called E2-instantons, to stabilise axion moduli and to repair the missing Yukawa couplings
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