## Abstract

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 Cl_{n}-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 language | English |
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Pages (from-to) | 1091-1143 |

Number of pages | 53 |

Journal | Reviews in Mathematical Physics |

Volume | 21 |

Issue number | 9 |

DOIs | |

Publication status | Published - Oct 2009 |

## Keywords

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