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

TL;DR

This paper reveals a surprising mathematical relation between effective coupling constants in N=2 supersymmetric Yang-Mills theories, connecting hyperelliptic curve descriptions with heterotic string lattice structures, hinting at a deeper duality.

Contribution

It establishes a new relation between theta functions of different lattices in the context of supersymmetric gauge theories, suggesting a universal extension of this relation.

Findings

The relation _{16}^+( au)=_8^2( au) holds for the coupling constants.

This relation mirrors T-duality between heterotic strings.

It likely extends to all curves describing effective supersymmetric gauge 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.