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

TL;DR

This paper demonstrates that all supersymmetric Type IIA D-branes can be constructed from unstable D9-branes, revealing that D-brane charges are classified by higher K-theory and linking Matrix theory dynamics to vortex physics on D9-branes.

Contribution

It establishes a string-theoretic construction of Type IIA D-branes using unstable D9-branes and identifies their charges with higher K-theory groups, connecting to Matrix theory.

Findings

D-brane charges classified by K^{-1}(X)

All D0-branes can be constructed from D9-branes

Matrix theory dynamics relate to vortex physics on D9-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.