Evidence for Heterotic/Heterotic Duality

TL;DR

The paper argues for a six-dimensional heterotic–heterotic duality of the $E_8\times E_8$ string on $K3$ with symmetric instanton embedding, proposing a self-duality that inverts the coupling and exchanges perturbative and non-perturbative gauge sectors. This duality is derived from M-theory on $K3\times S^1/{\bf Z}_2$ by considering two complementary limits, and it acts non-trivially on hypermultiplets while preserving anomaly consistency. The authors analyze unbroken gauge groups, small instanton physics, and the moduli of instanton configurations to illustrate how perturbative and non-perturbative sectors map into each other. They also establish a precise correspondence between worldsheet and spacetime loops, yielding non-renormalization constraints that support a robust dual dictionary with potential wide-ranging implications for dualities in string theory.

Abstract

We re-examine the question of heterotic - heterotic string duality in six dimensions and argue that the $E_8\times E_8$ heterotic string, compactified on $K3$ with equal instanton numbers in the two $E_8$'s, has a self-duality that inverts the coupling, dualizes the antisymmetric tensor, acts non-trivially on the hypermultiplets, and exchanges gauge fields that can be seen in perturbation theory with gauge fields of a non-perturbative origin. The special role of the symmetric embedding of the anomaly in the two $E_8$'s can be seen from field theory considerations or from an eleven-dimensional point of view. The duality can be deduced by looking in two different ways at eleven-dimensional $M$-theory compactified on $K3\times {\bf S}^1/\Z_2$.