Notes on Chern-Simons perturbation theory

被引:1
作者
Wernli, Konstantin [1 ]
机构
[1] Univ Southern Denmark, Ctr Quantum Math, Campusvej 55, DK-5230 Odense M, Denmark
关键词
Quantum field theory; Chern-Simons theory; Batalin-Vilkovisky formalism; perturbative quantization; effective actions; gauge theory; Feynman diagrams; anomalies; gauge invariance; homotopical methods in QFT; ANALYTIC TORSION; INTEGRAL INVARIANTS; GAUGE-THEORIES; R-TORSION; QUANTUM; QUANTIZATION; RENORMALIZATION; 3-MANIFOLDS; MANIFOLDS; DIAGRAMS;
D O I
10.1142/S0129055X22300035
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
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页数:89
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