The tiny order of magnitude of the cosmological constant is sought to be explained in a model involving the following ingredients: supersymmetry breaking in N=1 supergravity and the multiple point principle. We demonstrate the viability of this scenario in the minimal SUGRA model.

We propose a unification of some fine-tuning problems -really in this article only the problem of why the weak scale is so small in energy compared to a presumed fundamental scale, being say the Planck scale -by postulating the zero or very small value of the cosmological constant not only for one but for several vacua. This postulate corresponds to what we have called the Multiple Point Principle, namely that there be many "vacuum" states with the same energy density. We further assume that 6 top quarks and 6 anti-top quarks can bind by Higgs exchange so strongly as to become tachyonic and form a condensate. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The two vacua distinguished by such a condensate will have the same cosmological constant provided the top Yukawa coupling is about 1.1 ± 0.2, in good correspondence with the experimental value. The further requirement that this value of the Yukawa coupling, at the weak scale, be compatible with the existence of a third vacuum, with a Higgs field expectation value of the order of the fundamental scale, enforces a hierarchical scale ratio between the fundamental and weak scales of order 10 16 -10 20 .

The multiple point principle (MPP) is applied to the non-supersymmetric two-Higgs doublet extension of the Standard Model (SM). The existence of a large set of degenerate vacua at some high energy scale caused by the MPP results in a few relations between Higgs self-coupling constants which can be examined at future colliders. The numerical analysis reveals that these MPP conditions constrain the mass of the SM-like Higgs boson to lie below 180 GeV for a wide set of MPP scales Λ and tan β.

We propose a unification of some fine-tuning problems -really in this article only the problem of why the weak scale is so small in energy compared to a presumed fundamental scale, being say the Planck scale -by postulating the zero or very small value of the cosmological constant not only for one but for several vacua. This postulate corresponds to what we have called the Multiple Point Principle, namely that there be many "vacuum" states with the same energy density. We further assume that 6 top quarks and 6 anti-top quarks can bind by Higgs exchange so strongly as to become tachyonic and form a condensate. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The two vacua distinguished by such a condensate will have the same cosmological constant provided the top Yukawa coupling is about 1.1 ± 0.2, in good correspondence with the experimental value. The further requirement that this value of the Yukawa coupling, at the weak scale, be compatible with the existence of a third vacuum, with a Higgs field expectation value of the order of the fundamental scale, enforces a hierarchical scale ratio between the fundamental and weak scales of order 10 16 -10 20 .

The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants -electric α and magneticα -were obtained. It was shown that the Dirac relation is valid for the renormalized α andα at the arbitrary scale, but these RG equations can be considered perturbatively only in the small region: 0.25 . *