D-Branes in Orientifolds and Orbifolds and Kasparov KK-Theory

TL;DR

This paper classifies D-branes in orientifolds and orbifolds using Real and equivariant KK-theory, providing a unified mathematical framework and extending previous results on D-brane spectra and gauge theories.

Contribution

It introduces a KK-theoretic classification of D-branes in orientifolds and orbifolds, connecting physical D-brane configurations with advanced mathematical structures.

Findings

Classifies D-branes using Real and equivariant KK-groups.

Recovers and generalizes known D-brane spectra in orientifolds and orbifolds.

Computes gauge groups and properties of low energy effective theories.

Abstract

A classification of D-branes in Type IIB Op^- orientifolds and orbifolds in terms of Real and equivariant KK-groups is given. We classify D-branes intersecting orientifold planes from which are recovered some special limits as the spectrum for D-branes on top of Type I Op^- orientifold and the bivariant classification of Type I D-branes. The gauge group and transformation properties of the low energy effective field theory living in the corresponding unstable D-brane system are computed by extensive use of Clifford algebras. Some speculations about the existence of other versions of KK-groups, based on physical insights, are proposed. In the orbifold case, some known results concerning D-branes intersecting orbifolds are reproduced and generalized. Finally, the gauge theory of unstable systems in these orbifolds is recovered.