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Quantum curves and conformal field theory

Manabe, Masahide and Sułkowski, Piotr (2017) Quantum curves and conformal field theory. Physical Review D, 95 (12). Art. No. 126003. ISSN 2470-0010. doi:10.1103/PhysRevD.95.126003.

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To a given algebraic curve we assign an infinite family of quantum curves (Schrödinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model we build such quantum curves out of an appropriate representation of the Virasoro algebra, encoded in the structure of the α/β-deformed matrix integral and its loop equation. We generalize this construction to a large class of algebraic curves by means of a refined topological recursion. We also specialize this construction to various specific matrix models with polynomial and logarithmic potentials, and among other results, show that various ingredients familiar in the study of conformal field theory (Ward identities, correlation functions and a representation of Virasoro operators acting thereon, Belavin-Polyakov-Zamolodchikov equations) arise upon specialization of our formalism to the multi-Penner matrix model.

Item Type:Article
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URLURL TypeDescription Paper
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2017 American Physical Society. Received 13 March 2017; published 6 June 2017. We thank Hidetoshi Awata, Hiroyuki Fuji, Kohei Iwaki, Zbigniew Jaskólski, Hiroaki Kanno, Ivan Kostov, Motohico Mulase, and Marcin Piątek for insightful discussions and comments on the manuscript. We very much appreciate hospitality of the Simons Center for Geometry and Physics where parts of this work were done. This work is supported by the European Research Council Starting Grant no. 335739 “Quantum fields and knot homologies” funded by the European Research Council under the European Union’s Seventh Framework Programme, and the Ministry of Science and Higher Education in Poland.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)335739
Ministry of Science and Higher Education (Poland)UNSPECIFIED
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Issue or Number:12
Record Number:CaltechAUTHORS:20160113-131903649
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:63646
Deposited By: Joy Painter
Deposited On:13 Jan 2016 21:29
Last Modified:10 Nov 2021 23:19

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