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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.

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.