Lecture Notes on Chern-Simons Perturbation Theory

Abstract

The goal of these lectures is to exhibit the framing anomaly in the Batalin-Vilkovisky formulation of perturbative Chern-Simons theory. Concretely, we show that the partition function fails to satisfy the Quantum Master Equation, and show that this can be remedied at the cost of introducing a framing. Along the way, we discuss principal bundles and connections, the Chern-Simons action functional, and perturbative quantization of gauge theories in the Batalin-Vilkovisky formalism.

These are the notes for a lecture series given at KMPG at Humboldt-Universität Berlin in Summer 2019. Comments appreciated

References in corpus (4)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• An introduction to the Batalin-Vilkovisky formalism
• On the Kontsevich-Kuperberg-Thurston construction of a configuration-space invariant for rational homology 3-spheres
• On the coordinate (in)dependence of the formal path integral