D-branes and KK-theory in Type I String Theory

TL;DR

This paper explores unstable D-brane systems in type I string theory, linking their classification to real KK-theory, and constructs explicit D-brane solutions using Clifford algebra within boundary string field theory.

Contribution

It provides a physical interpretation of real KK-theory for classifying D-branes and systematically describes the field content using Clifford algebra, extending previous proposals.

Findings

D-branes in product spaces are classified by real KK-theory groups.

Spectrum of D-branes matches expectations, including stable non-BPS D-branes with Z_2 charge.

Explicit D-brane solutions are constructed within boundary string field theory.

Abstract

We analyse unstable D-brane systems in type I string theory. Generalizing the proposal in hep-th/0108085, we give a physical interpretation for real KK-theory and claim that the D-branes embedded in a product space X x Y which are made from the unstable Dp-brane system wrapped on Y are classified by a real KK-theory group KKO^{p-1}(X,Y). The field contents of the unstable D-brane systems are systematically described by a hidden Clifford algebra structure. We also investigate the matrix theory based on non-BPS D-instantons and show that the spectrum of D-branes in the theory is exactly what we expect in type I string theory, including stable non-BPS D-branes with Z_2 charge. We explicitly construct the D-brane solutions in the framework of BSFT and analyse the physical property making use of the Clifford algebra.