Abstract
We compute partition functions of Chern-Simons type theories for cylindrical spacetimes I × Σ , with I an interval and dimΣ = 4l + 2 , in the BV-BFV formalism (a refinement of the Batalin-Vilkovisky formalism adapted to manifolds with boundary and cutting-gluing). The case dimΣ = 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 (Cattaneo et al., Constrained systems, generalized Hamilton-Jacobi actions, and quantization, arXiv:2012.13270), without any quantum corrections. This Hamilton-Jacobi action is the action functional of a conformal field theory on Σ . For dimΣ = 2 , this implies a version of the CS-WZW correspondence. For dimΣ = 6 , using a particular polarization on one end of the cylinder, the Chern-Simons partition function is related to Kodaira-Spencer gravity (a.k.a. BCOV theory); this provides a BV-BFV quantum perspective on the semiclassical result by Gerasimov and Shatashvili.