D-Brane Instantons and K-Theory Charges

TL;DR

This paper explores the physical interpretation of K-theory classification of D-brane charges through the lens of D-instantons, linking mathematical algorithms to physical phenomena and applying these ideas to branes in WZW models.

Contribution

It provides a physical perspective on K-theoretic classification of D-branes using D-instantons and proposes a formulation of K-homology based on this approach.

Findings

Relation between D-instantons and K-theory algorithms clarified

Application to D-brane charges in WZW models demonstrated

Detailed analysis of SU(3) case and insights into SU(N) branes

Abstract

We discuss some physical issues related to the K-theoretic classification of D-brane charges, putting an emphasis on the role of D-brane instantons. The relation to D-instantons provides a physical interpretation to the mathematical algorithm for computing K-theory known as the ``Atiyah-Hirzebruch spectral sequence.'' Conjecturally, a formulation in terms of D-instantons leads to a computationally useful formulation of K-homology in general. As an application and illustration of this viewpoint we discuss some issues connected with D-brane charges associated with branes in WZW models. We discuss the case of SU(3) in detail, and comment on the general picture of branes in SU(N), based on a recent result of M. Hopkins.