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

Abstract

We show that the effective coupling constants $\tau$ 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 $$ \Theta_{D_{16}^+}(\tau)=\Theta_{E_8}^2(\tau) $$ 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.