Heriot-Watt Mathematics Report Series
HWM06-40, 13 Oct 2006

KO-Homology and Type I String Theory

R M G Reis, R J Szabo and A Valentino


Abstract

We study the classification of D-branes and Ramond-Ramond fields in Type I string theory by developing a geometric description of KO-homology, analogous to the Baum-Douglas construction. We define an analytic version of KO-homology using KK-theory of real C^*-algebras, and construct explicitly the isomorphism between geometric and analytic KO-homology. The construction involves a certain geometric invariant which is used, along with a definition of the real Chern character in KO-homology, to derive cohomological index formulas in certain dimensions. We show that this invariant also naturally assigns torsion charges to non-BPS states in Type I string theory, in the construction of classes of D-branes in terms of topological KO-cycles. The formalism also naturally captures the coupling of Ramond-Ramond fields to background D-branes which cancel global anomalies in the string path integral. We argue that this is related to a physical interpretation of bivariant KK-theory. We also provide a construction of the holonomies of Ramond-Ramond fields in terms of topological KO-chains.

Google Scholar Search: links, citations and journal (if available)


Contact Details | 2006 Reports Index | Full Index