Type IIA D-Branes, K-Theory, and Matrix Theory

TL;DR

This work shows that all supersymmetric Type IIA D-branes can be constructed as bound states of unstable Type IIA D9-branes, with D-brane charges on a spacetime $X$ classified by the higher K-theory group $K^{-1}(X)$. The tachyonic dynamics on the worldvolume of a system of 16 spacetime-filling 9-branes yields vortex-monopole configurations that realize D0-branes and more generally all D-branes as bound states, linking string theory to K-theory and offering a holographic-like Matrix theory interpretation as vortex dynamics on a fixed 9-brane system. The construction naturally generalizes to orientifold setups via KR^{-1}(X) and suggests deep connections between M-theory extensions and K-theory definitions. Overall, the paper provides a concrete, symmetry-preserving bound-state framework for Type IIA D-branes and a novel viewpoint on Matrix theory through non-supersymmetric gauge theory on 9-branes.

Abstract

We show that all supersymmetric Type IIA D-branes can be constructed as bound states of a certain number of unstable non-supersymmetric Type IIA D9-branes. This string-theoretical construction demonstrates that D-brane charges in Type IIA theory on spacetime manifold $X$ are classified by the higher K-theory group $K^{-1}(X)$, as suggested recently by Witten. In particular, the system of $N$ D0-branes can be obtained, for any $N$, in terms of sixteen Type IIA D9-branes. This suggests that the dynamics of Matrix theory is contained in the physics of magnetic vortices on the worldvolume of sixteen unstable D9-branes, described at low energies by a U(16) gauge theory.