D-branes, matrix theory and K-homology

In this paper, we study a new matrix theory based on non-BPS D-instantons intype IIA string theory and D-instanton - anti D-instanton system in type IIBstring theory, which we call K-matrix theory. The theory correctly incorporatesthe creation and annihilation processes of D-branes. The configurations of thetheory are identified with spectral triples, which are the noncommutativegeneralization of Riemannian geometry a la Connes, and they represent thegeometry on the world-volume of higher dimensional D-branes. Remarkably, theconfigurations of D-branes in the K-matrix theory are naturally classified by aK-theoretical version of homology group, called K-homology. Furthermore, weargue that the K-homology correctly classifies the D-brane configurations froma geometrical point of view. We also construct the boundary statescorresponding to the configurations of the K-matrix theory, and explicitly showthat they represent the higher dimensional D-branes.Comment: 53 pages, corrected a few typos, version published in JHE