## Abstract

We give a detailed introduction to the classical Chern-Simons gauge theory, including the mathematical preliminaries. We then explain the perturbative quantization of gauge theories via the Batalin-Vilkovisky (BV) formalism. We then define the perturbative Chern-Simons partition function at any (possibly non-acylic) reference flat connection using the BV formalism, using a Riemannian metric for gauge fixing. We show that it exhibits an anomaly known as the "framing anomaly"when the Riemannian metric is changed, that is, it fails to be gauge invariant. We explain how one can deal with this anomaly to obtain a topological invariant of framed manifolds.

Original language | English |
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Article number | 2230003 |

Journal | Reviews in Mathematical Physics |

Volume | 34 |

Issue number | 3 |

ISSN | 0129-055X |

DOIs | |

Publication status | Published - Apr 2022 |

## Keywords

- Anomalies
- Batalin-Vilkovisky formalism
- Chern-Simons theory
- Effective actions
- Feynman diagrams
- Gauge invariance
- Gauge theory
- Homotopical methods in QFT
- Perturbative quantization
- Quantum field theory
- effective actions
- anomalies
- homotopical methods in QFT
- gauge theory
- perturbative quantization
- gauge invariance