Quantum Chern-Simons theories on cylinders: BV-BFV partition functions

Understand

We compute partition functions of Chern-Simons type theories for cylindrical spacetimes $I \times \Sigma$, with $I$ an interval and $\dim \Sigma = 4l+2$, in the BV-BFV formalism (a refinement of the Batalin-Vilkovisky formalism adapted to manifolds with boundary and cutting-gluing).

• The case $\dim \Sigma = 0$ is considered as a toy example.
• We show that one can identify - for certain choices of residual fields - the "physical part" (restriction to degree zero fields) of the BV-BFV effective action with the Hamilton-Jacobi action computed in the companion paper [arXiv:2012.13270], without any quantum corrections.
• This Hamilton-Jacobi action is the action functional of a conformal field theory on $\Sigma$.