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

We compute partition functions of Chern–Simons type theories for cylindrical spacetimes [Formula: see text] , with I an interval and [Formula: see text] , in the BV-BFV formalism (a refinement of the Batalin–Vilkovisky formalism adapted to manifolds with boundary and cutting–gluing). The case [Formu...

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Detalles Bibliográficos
Autores principales: Cattaneo, Alberto S., Mnev, Pavel, Wernli, Konstantin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9898435/
https://www.ncbi.nlm.nih.gov/pubmed/36751404
http://dx.doi.org/10.1007/s00220-022-04513-8
Descripción
Sumario:We compute partition functions of Chern–Simons type theories for cylindrical spacetimes [Formula: see text] , with I an interval and [Formula: see text] , in the BV-BFV formalism (a refinement of the Batalin–Vilkovisky formalism adapted to manifolds with boundary and cutting–gluing). The case [Formula: see text] 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 [Formula: see text] . For [Formula: see text] , this implies a version of the CS-WZW correspondence. For [Formula: see text] , 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.