Notes on Chern-Simons perturbation theory

Konstantin Wernli*

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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.

OriginalsprogEngelsk
Artikelnummer2230003
TidsskriftReviews in Mathematical Physics
Vol/bind34
Udgave nummer3
ISSN0129-055X
DOI
StatusUdgivet - apr. 2022

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