Evidence for heterotic/heterotic duality

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.