Ko-Homology and type i string theory

R. M G Reis, Richard J. Szabo, Alessandro Valentino

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We study the classification of D-branes and RamondRamond fields in Type I string theory by developing a geometric description of KO-homology. 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 recasting the Cln-index theorem and a certain geometric invariant into a homological framework which is used, along with a definition of the real Chern character in KO-homology, to derive cohomological index formulas. 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 naturally captures the coupling of RamondRamond fields to background D-branes which cancel global anomalies in the string theory path integral. We show that this is related to a physical interpretation of bivariant KK-theory in terms of decay processes on spacetime-filling branes. We also provide a construction of the holonomies of RamondRamond fields in Type II string theory in terms of topological K-chains. © 2009 World Scientific Publishing Company.

Original languageEnglish
Pages (from-to)1091-1143
Number of pages53
JournalReviews in Mathematical Physics
Issue number9
Publication statusPublished - Oct 2009


  • Classification of D-branes
  • Index theory
  • KO-homology
  • Type I string theory


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