Geometric K-Homology of Flat D-Branes

TL;DR

This paper applies topological K-homology to analyze D-branes in Type II superstring theory, providing explicit descriptions, stability criteria, and flux stabilization mechanisms, along with new mathematical insights.

Contribution

It introduces a K-homology framework for D-branes, deriving stability conditions and flux stabilization, and presents new results in topological K-homology.

Findings

Explicit K-homology descriptions of D-branes

Stability criteria for D-brane states

Flux stabilization via K-homology of fibre bundles

Abstract

We use the Baum-Douglas construction of K-homology to explicitly describe various aspects of D-branes in Type II superstring theory in the absence of background supergravity form fields. We rigorously derive various stability criteria for states of D-branes and show how standard bound state constructions are naturally realized directly in terms of topological K-cycles. We formulate the mechanism of flux stabilization in terms of the K-homology of non-trivial fibre bundles. Along the way we derive a number of new mathematical results in topological K-homology of independent interest.