Quantum Chern-Simons Theories on Cylinders: BV-BFV Partition Functions.

We compute partition functions of Chern-Simons type theories for cylindrical spacetimes , with an interval and , in the BV-BFV formalism (a refinement of the Batalin-Vilkovisky formalism adapted to manifolds with boundary and cutting-gluing). The case 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 (Cattaneo et al.