Instantons on D-branes

TL;DR

This paper explores instanton effects on D-branes in type IIA string theory compactified on K3, revealing a Hagedorn density of BPS states and connecting to affine Kac-Moody algebras via heterotic-type IIA duality.

Contribution

It demonstrates the instanton subsectors of D4-branes on K3 lead to a Hagedorn density of BPS states and links Nakajima's algebraic structures to heterotic-type IIA duality.

Findings

Hagedorn density of BPS states in D-brane instanton sectors

Connection between Nakajima's affine Kac-Moody algebras and heterotic duality

Evidence supporting heterotic-type IIA duality in 6D compactifications

Abstract

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.