Quantum chern–simons theories on cylinders: BV-BFV Partition Functions

Alberto S. Cattaneo*, Pavel Mnev, Konstantin Wernli


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We compute partition functions of Chern–Simons type theories for cylindrical spacetimes I× Σ , with I an interval and dim Σ = 4 l+ 2 , in the BV-BFV formalism (a refinement of the Batalin–Vilkovisky formalism adapted to manifolds with boundary and cutting–gluing). The case dim Σ = 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 dim Σ = 2 , this implies a version of the CS-WZW correspondence. For dim Σ = 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.

TidsskriftCommunications in Mathematical Physics
Udgave nummer1
Sider (fra-til)133-218
StatusUdgivet - 2023

Bibliografisk note

Funding Information:
This research was (partly) supported by the NCCR SwissMAP, funded by the Swiss National Science Foundation. A.S.C. and K.W. acknowledge partial support of SNF Grants No. 200020_192080 and 200020_172498/1. K. W. also acknowledges support from a BMS Dirichlet postdoctoral fellowship and the SNF Postdoc.Mobility grant P2ZHP2_184083, and would like to thank the Humboldt-Universität Berlin, in particular the group of Dirk Kreimer, and the university of Notre Dame for their hospitality. .

Publisher Copyright:
© 2022, The Author(s).


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