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arXiv · 2012.13983

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

Alberto S. Cattaneo·Pavel Mnev·Konstantin Wernli
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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.

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Alberto S. Cattaneo, Pavel Mnev, Konstantin Wernli. 2020-12-27. Quantum Chern-Simons theories on cylinders: BV-BFV partition functions. https://doi.org/10.1007/s00220-022-04513-8

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