Brane Descent Relations in K-theory

TL;DR

This paper classifies D-brane descent and duality relations using topological K-theory, revealing new internal descent relations and their connection to topological solitons and Hopf fibrations.

Contribution

It introduces a comprehensive K-theoretic framework for D-brane relations, including new internal descent relations and their extension to orientifolds and type-I theories.

Findings

Classification of descent and duality relations via K-theory

Discovery of new internal descent relations for orientifold planes

Connection of brane charges to topological solitons and Hopf fibrations

Abstract

The various descent and duality relations among BPS and non-BPS D-branes are classified using topological K-theory. It is shown how the descent procedures for producing type-II D-branes from brane-antibrane bound states by tachyon condensation and $\klein$ projections arise as natural homomorphisms of K-groups generating the brane charges. The transformations are generalized to type-I theories and type-II orientifolds, from which the complete set of vacuum manifolds and field contents for tachyon condensation is deduced. A new set of internal descent relations is found which describes branes over orientifold planes as topological defects in the worldvolumes of brane-antibrane pairs on top of planes of higher dimension. The periodicity properties of these relations are shown to be a consequence of the fact that all fundamental bound state constructions and hence the complete spectrum of brane charges are associated with the topological solitons which classify the four Hopf fibrations.