A Surprising Relation for the Effective Coupling Constants of N=2 Super Yang-Mills Theories

We show that the effective coupling constants $τ$ of supersymmetric gauge theories described by hyperelliptic curves do not distinguish between the lattices of the two kinds of heterotic string. In particular, the following relation $Θ_{D_{16}^+}(τ)=Θ_{E_8}^2(τ)$ holds. This is reminiscent of the relation, by $T$-duality, of the two heterotic strings. We suggest that such a relation extends to all curves describing effective supersymmetric gauge theories.

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