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From CFT to Ramond super-quantum curves

Ciosmak, Paweł and Hadasz, Leszek and Jaskólski, Zbigniew and Manabe, Masahide and Sułkowski, Piotr (2018) From CFT to Ramond super-quantum curves. Journal of High Energy Physics, 2018 (5). Art. No. 133. ISSN 1126-6708. doi:10.1007/JHEP05(2018)133.

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As we have shown in the previous work, using the formalism of matrix and eigenvalue models, to a given classical algebraic curve one can associate an infinite family of quantum curves, which are in one-to-one correspondence with singular vectors of a certain (e.g. Virasoro or super-Virasoro) underlying algebra. In this paper we reformulate this problem in the language of conformal field theory. Such a reformulation has several advantages: it leads to the identification of quantum curves more efficiently, it proves in full generality that they indeed have the structure of singular vectors, it enables identification of corresponding eigenvalue models. Moreover, this approach can be easily generalized to other underlying algebras. To illustrate these statements we apply the conformal field theory formalism to the case of the Ramond version of the super-Virasoro algebra. We derive two classes of corresponding Ramond super-eigenvalue models, construct Ramond super-quantum curves that have the structure of relevant singular vectors, and identify underlying Ramond super-spectral curves. We also analyze Ramond multi-Penner models and show that they lead to supersymmetric generalizations of BPZ equations.

Item Type:Article
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URLURL TypeDescription Paper
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: January 23, 2018; Accepted: May 5, 2018; Published: May 22, 2018. This work is supported by the ERC 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. The work of PC is also supported by the National Science Centre, Poland Preludium grant no. 2016/23/N/ST1/01250 “Quantum curves and Schrödinger equations in matrix models”. The work of MM is also supported by the Max-Planck-Institut für Mathematik in Bonn.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)335739
Ministry of Science and Higher Education (Poland)UNSPECIFIED
National Science Centre (Poland)2016/23/N/ST1/01250
Max-Planck-Institut für MathematikUNSPECIFIED
Subject Keywords:Conformal Field Theory; Matrix Models
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Issue or Number:5
Record Number:CaltechAUTHORS:20180109-163133399
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Official Citation:Ciosmak, P., Hadasz, L., Jaskólski, Z. et al. J. High Energ. Phys. (2018) 2018: 133.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84215
Deposited By: Joy Painter
Deposited On:10 Jan 2018 00:38
Last Modified:15 Nov 2021 20:17

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