Lecture Notes on Chern-Simons Perturbation Theory

TL;DR

This paper explains the framing anomaly in perturbative Chern-Simons theory using the Batalin-Vilkovisky formalism, showing how the partition function's failure to satisfy the Quantum Master Equation can be fixed by introducing a framing.

Contribution

It provides a detailed exposition of the framing anomaly in the Batalin-Vilkovisky approach to Chern-Simons theory, linking the anomaly to the Quantum Master Equation.

Findings

Partition function fails to satisfy the Quantum Master Equation without framing.

Introducing a framing remedies the failure, ensuring consistency.

Discussion of principal bundles, connections, and perturbative quantization methods.

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.