A surprising relation for the effective coupling constants of N = 2 super Yang-Mills theories

摘要

A bstract 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 $$ {arTheta}_{D_{16}^{+}}left(au ight)={arTheta}_{E_8}^2left(au ight) $$ 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.