### 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) |
---|---|

Pages (from-to) | 1197-1240 |

Number of pages | 44 |

Journal | Reviews in Mathematical Physics |

Volume | 21 |

Issue number | 10 |

DOIs | |

State | Published - Nov 1 2009 |

### Fingerprint

### 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

### Cite this

*Reviews in Mathematical Physics*,

*21*(10), 1197-1240. https://doi.org/10.1142/S0129055X09003840

**Fivebrane structures.** / Sati, Hisham; Schreiber, Urs; Stasheff, Jim.

Research output: Contribution to journal › Article

*Reviews in Mathematical Physics*, vol. 21, no. 10, pp. 1197-1240. https://doi.org/10.1142/S0129055X09003840

}

TY - JOUR

T1 - Fivebrane structures

AU - Sati, Hisham

AU - Schreiber, Urs

AU - Stasheff, Jim

PY - 2009/11/1

Y1 - 2009/11/1

N2 - 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.

AB - 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.

KW - Anomaly

KW - Fivebrane

KW - Generalizations of fiber spaces and bundles

KW - Obstruction theory

KW - String theory

KW - Superstring theory

UR - http://www.scopus.com/inward/record.url?scp=71249099888&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71249099888&partnerID=8YFLogxK

U2 - 10.1142/S0129055X09003840

DO - 10.1142/S0129055X09003840

M3 - Article

AN - SCOPUS:71249099888

VL - 21

SP - 1197

EP - 1240

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 10

ER -