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

Abstract

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 $\Sigma$. For $\dim \Sigma =2$, this implies a version of the CS-WZW correspondence. For $\dim \Sigma =6$, 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.

81 pages, 11 figures. v.2: updated references. v.3: small expository changes

References in corpus (4)

• Averaging Over Narain Moduli Space
• Quantization of open-closed BCOV theory, I
• Constrained systems, generalized Hamilton-Jacobi actions, and quantization
• Discrete BF theory

Cited by in corpus (5)

• Constrained systems, generalized Hamilton-Jacobi actions, and quantization
• 5d-4d Correspondence in Twisted M-theory on a Conifold
• The linear CS/WZW bulk/boundary system in AQFT
• Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism