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A new universal model to implement the Seiberg–Witten approach to low-energy properties of the supersymmetric N = 2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It is based on the hyperelliptic curve, whose genus equals the rank of the gauge group. The weak and strong coupling limits are reproduced. The magnetic and electric charges of light dyons, which are present in the proposed model comply with recent predictions derived from the general properties of the theory. The discrete chiral symmetry is implemented, the duality condition is reproduced, and connections between monodromies at weak and strong coupling are established. It is found that the spectra of monopoles and dyons are greatly simplified when vectors representing the scalar and dual fields in the Cartan algebra are aligned along the Weyl vector. This general feature of the theory is used for an additional verification of the model. The model predicts the identical analytic structures of the coupling constants for the theories based on the SU ( r + 1 ) and Sp ( 2 r ) gauge groups.

In the Standard Model, a group of heavy fermions, e.g. top quarks, can collectively strongly affect the Higgs field and create relatively long-lived bound states. If there exist new generations of fermions with masses beyond 1 TeV, strong binding of several of them can make them lighter than even a single heavy fermion. Using the mean field approximation we find multi-fermion states with masses M ∼ 5 v N ≈ 1.2 N TeV , with N = 2 , 3 , … and v = 246 GeV being the total number of heavy fermions bound together, and the Higgs VEV. These results inspire a hope that the experimental search for multi-fermions within the range of energies 2–3 Tev would either discover them, or suggest absence of new Standard Model fermions with larger masses. Possible implications related to multi-top states and baryonic asymmetry of the Universe are discussed.

Expressions for electric and magnetic charges of dyons, which become massless in the strong-coupling limit of the supersymmetric N = 2 gauge theory with an arbitrary gauge group are presented. Transitions into different vacua of the N = 1 gauge theory, when the N = 2 supersymmetry is broken explicitly to the N = 1 case, are discussed. The existence of a minimal set of light dyons, which are necessary to describe this transition, is established. The total number of these dyons equals the product of the rank and dual Coxeter number of the gauge group. A conjecture, which states that this minimal set incorporates all possible light dyons, is discussed. A relation of dyon charges with monodromies at weak and strong couplings is outlined and comparison with known charges of dyons for particular gauge groups is made.

The Coulomb problem for vector bosons W incorporates a known difficulty; the boson falls on the center. In QED the fermion vacuum polarization produces a barrier at small distances which solves the problem. In a renormalizable SU(2) theory containing vector triplet (W^+,W^-,gamma) and a heavy fermion doublet F with mass M the W^- falls on F^+, to distances r ~ 1/M, where M can be made arbitrary large. To prevent the collapse the theory needs additional light fermions, which switch the ultraviolet behavior of the theory from the asymptotic freedom to the Landau pole. Similar situation can take place in the Standard Model. Thus, the renormalizability of a theory is not sufficient to guarantee a reasonable behavior at small distances for non-perturbative problems, such as a bound state problem., Comment: Four pages

The behavior of fermions in the gauge field created by the energon, a recently found classical solution of the non-Abelian gauge theory, is considered. The spectrum of fermions is evaluated explicitly for the case when parameters governing the energon are chosen to make this solution look similar to the chain of well separated instantons and anti-instantons. The zero eigenvalue in the spectrum of the Dirac equation is found. The role of a specific discrete symmetry, which distinguishes the energon, is discussed., 7 pages

We discuss a new family of multiquanta-bound states in the standard model which exist due to the mutual Higgs-based attraction of the heaviest members of the standard model, namely, gauge quanta W, Z, and (anti)top quarks, t, t. We use a self-consistent mean-field approximation, up to a rather large particle number N. In this paper we do not focus on weakly bound, nonrelativistic bound states, but rather on 'bags' in which the Higgs vacuum expectation value is significantly modified or depleted. The minimal number N above which such states appear strongly depends on the ratio of the Higgs mass to the masses of W, Z, t, t: For a light Higgs mass, m{sub H{approx}}50 GeV, bound states start from N{approx}O(10), but for a ''realistic'' Higgs mass, m{sub H{approx}}100 GeV, one finds metastable/bound W, Z bags only for N{approx}O(1000). We also found that in the latter case pure top bags disappear for all N, although top quarks can still be well bound to the W bags. Anticipating the cosmological applications (discussed in the following Article [Phys. Rev. D 82, 073019]) of these bags as 'doorway states' for baryosynthesis, we also consider here the existence of such metastable bags at finite temperatures,more » when standard-model parameters such as Higgs, gauge, and top masses are significantly modified.« less