## Abstract

We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H^{4}(BG, Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H^{3}(G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map from H^{4}(BG, Z) to H^{3}(G, Z). We generalize this correspondence to topological "spin" theories, which are defined on three manifolds with spin structure, and are related to what might be called Z_{2} graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.

Original language | English (US) |
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Pages (from-to) | 393-429 |

Number of pages | 37 |

Journal | Communications In Mathematical Physics |

Volume | 129 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1990 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics