D-branes, Matrix Theory and K-homology

Details D-branes, Matrix Theory and K-homology D-branes, Matrix Theory and K-homology

2001-08-13

arxiv.org/abs/hep-th/0108085v3

JHEP 0203 (2002) 034

Physics

High Energy Physics

High Energy Physics - Theory

53 pages, corrected a few typos, version published in JHEP

Scientific paper

10.1088/1126-6708/2002/03/034

In this paper, we study a new matrix theory based on non-BPS D-instantons in type IIA string theory and D-instanton - anti D-instanton system in type IIB string theory, which we call K-matrix theory. The theory correctly incorporates the creation and annihilation processes of D-branes. The configurations of the theory are identified with spectral triples, which are the noncommutative generalization of Riemannian geometry a la Connes, and they represent the geometry on the world-volume of higher dimensional D-branes. Remarkably, the configurations of D-branes in the K-matrix theory are naturally classified by a K-theoretical version of homology group, called K-homology. Furthermore, we argue that the K-homology correctly classifies the D-brane configurations from a geometrical point of view. We also construct the boundary states corresponding to the configurations of the K-matrix theory, and explicitly show that they represent the higher dimensional D-branes.

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