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

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.

💡 Research Summary

The paper develops a comprehensive categorical framework for classifying D‑brane charges on non‑commutative manifolds by employing bivariant K‑theory, specifically Kasparov’s KK‑theory. The authors begin by modeling a non‑commutative space as a C∗‑algebra (A) and identifying D‑branes with objects in the category of (right) (A)‑modules. Instead of the traditional K‑theory groups (K_0(A)) and (K_1(A)), which are insufficient for capturing Morita‑invariant data in the non‑commutative setting, they propose that the fundamental charge class lives in (KK(A,\mathbb{C})). This class (