## Abstract

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the GreenSchwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.

Original language | English (US) |
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Pages (from-to) | 1197-1240 |

Number of pages | 44 |

Journal | Reviews in Mathematical Physics |

Volume | 21 |

Issue number | 10 |

DOIs | |

State | Published - Nov 2009 |

## Keywords

- Anomaly
- Fivebrane
- Generalizations of fiber spaces and bundles
- Obstruction theory
- String theory
- Superstring theory

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics