$K$-theoretic matching of brane charges in S- and U-duality

Abstract

We discuss $K$-theoretic matching of $D$-brane charges in the string duality between type I on ${\mathbb T}^4$ and type IIA on $K3$. This case is more complex than the familiar case of IIA/IIB duality, which is already well understood, but it turns out that replacing $K3$ by its orbifold blow-down seems to largely resolve the apparent problems with the theory.