Notes on Chern-Simons perturbation theory

Konstantin Wernli*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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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 languageEnglish
Article number2230003
JournalReviews in Mathematical Physics
Issue number3
Publication statusPublished - Apr 2022


  • 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


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