D-brane charges and K-homology

TL;DR

This paper proposes that D-brane charges are classified by K-homology, providing a mathematical framework that explains phase factors in string theory partition functions for smooth spin manifolds.

Contribution

It introduces K-homology as the natural setting for D-brane charges, linking geometric and topological aspects of string theory.

Findings

D-brane charges are in K-homology.

K-homology explains phase factors in string theory.

Connection between D-branes and topological K-theory.

Abstract

It is argued that D-brane charge takes values in K-homology. For smooth manifolds with spin structure, this could explain why the phase factor $\Omega(x)$ calculated with a D-brane state x in IIB theory appears in Diaconescu, Moore and Witten's computation of the partition function of IIA string theory.