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arXiv · hep-th/0108085

D-branes, Matrix Theory and K-homology

T. Asakawa·S. Sugimoto·S. Terashima
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Abstract

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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T. Asakawa, S. Sugimoto, S. Terashima. 2002-04-08. D-branes, Matrix Theory and K-homology. https://doi.org/10.1088/1126-6708%2F2002%2F03%2F034

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