Split Chern-Simons theory in the BV-BFV formalism

TL;DR

This paper provides an overview of the BV-BFV formalism for quantizing boundary-including field theories and illustrates it with a new example of Chern-Simons theory.

Contribution

It introduces a specific application of the BV-BFV formalism to Chern-Simons theory, expanding the framework's practical examples.

Findings

Demonstrated perturbative quantization of Chern-Simons theory with boundary

Extended the BV-BFV formalism to a new example in gauge theory

Provided insights into boundary effects in topological quantum field theories

Abstract

The goal of this note is to give a brief overview of the BV-BFV formalism developed by the first two authors and Reshetikhin in [arXiv:1201.0290], [arXiv:1507.01221] in order to perform perturbative quantisation of Lagrangian field theories on manifolds with boundary, and present a special case of Chern-Simons theory as a new example.