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

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(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. e-print archive: http://xxx.lanl.gov/abs/hep-th/9812135 1374 TYPE IIA D-BRANES, K-THEORY, AND MATRIX THEORY