Instantons on D-branes

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We consider type IIA compactification on K3. We show that the instanton subsectors of the worldvolume of N 4-branes wrapped around K3 lead to a Hagedorn density of BPS states in accord with heterotic-type IIA duality in 6 dimensions. We also find evidence that the correct framework to understand the results of Nakajima on the appearance of affine Kac-Moody algebras on the cohomology of moduli space of instantons on ALE spaces is in the context of heterotic-type IIA string duality.