D-branes, KK-theory and duality on noncommutative spaces

TL;DR

This paper introduces a categorical framework using bivariant K-theory to classify D-brane charges on noncommutative spaces, with applications to charge formulas, T-duality, and anomaly cancellation.

Contribution

It develops a novel classification approach for D-branes on noncommutative manifolds leveraging bivariant K-theory, expanding the mathematical tools in string theory.

Findings

Derived an explicit D-brane charge formula in cyclic homology

Refined the understanding of open string T-duality

Provided a criterion for global anomaly cancellation

Abstract

We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology, a refinement of open string T-duality, and a general criterion for cancellation of global worldsheet anomalies.