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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2022
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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 |
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. |
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