## Abstract

A general formula for global gauge and gravitational anomalies is derived. It is used to show that the anomaly free supergravity and superstring theories in ten dimensions are all free of global anomalies that might have ruined their consistency. However, it is shown that global anomalies lead to some restrictions on allowed compactifications of these theories. For example, in the case of O(32) superstring theory, it is shown that a global anomaly related to π_{7}(O(32)) leads to a Dirac-like quantization condition for the field strength of the antisymmetric tensor field. Related to global anomalies is the question of the number of fermion zero modes in an instanton field. It is argued that the relevant gravitational instantons are exotic spheres. It is shown that the number of fermion zero modes in an instanton field is always even in ten dimensional supergravity.

Original language | English (US) |
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Pages (from-to) | 197-229 |

Number of pages | 33 |

Journal | Communications In Mathematical Physics |

Volume | 100 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1985 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics