### 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 |
---|---|

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 |

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### Keywords

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

### Cite this

*Reviews in Mathematical Physics*,

*21*(9), 1091-1143. https://doi.org/10.1142/S0129055X09003839

}

*Reviews in Mathematical Physics*, vol. 21, no. 9, pp. 1091-1143. https://doi.org/10.1142/S0129055X09003839

**Ko-Homology and type i string theory.** / Reis, R. M G; Szabo, Richard J.; Valentino, Alessandro.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Ko-Homology and type i string theory

AU - Reis, R. M G

AU - Szabo, Richard J.

AU - Valentino, Alessandro

PY - 2009/10

Y1 - 2009/10

N2 - 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.

AB - 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.

KW - Classification of D-branes

KW - Index theory

KW - KO-homology

KW - Type I string theory

UR - http://www.scopus.com/inward/record.url?scp=70449112779&partnerID=8YFLogxK

U2 - 10.1142/S0129055X09003839

DO - 10.1142/S0129055X09003839

M3 - Article

VL - 21

SP - 1091

EP - 1143

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 9

ER -