D-branes, Matrix Theory and K-homology

TL;DR

This paper introduces K-matrix theory, a new matrix framework based on non-BPS D-instantons and D-instanton-anti D-instanton systems, which classifies D-brane configurations using K-homology and connects noncommutative geometry with string theory.

Contribution

It develops K-matrix theory incorporating brane creation and annihilation, and establishes a classification of D-branes via K-homology, linking noncommutative geometry with string theory.

Findings

K-matrix theory correctly models D-brane creation and annihilation.

D-brane configurations are classified by K-homology.

Boundary states explicitly represent higher-dimensional D-branes.

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.