A Caltech Library Service

Super-quantum curves from super-eigenvalue models

Ciosmak, Paweł and Hadasz, Leszek and Manabe, Masahide and Sułkowski, Piotr (2016) Super-quantum curves from super-eigenvalue models. Journal of High Energy Physics, 2016 (10). Art. No. 044. ISSN 1126-6708. doi:10.1007/JHEP10(2016)044.

[img] PDF - Published Version
Creative Commons Attribution.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2016 The Author(s). 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: August 28, 2016; Accepted: October 4, 2016; Published: October 10, 2016. We thank Vincent Bouchard, Zbigniew Jaskólski, Motohico Mulase and Chaiho Rim for discussions and comments on the manuscript. We thank Simons Center for Geometry and Physics and C. N. Yang Institute for Theoretical Physics, Stony Brook, NY, for hospitality and support. 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.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)335739
Ministry of Science and Higher Education (Poland)UNSPECIFIED
Subject Keywords:Matrix Models, Conformal and W Symmetry, 2D Gravity, Topological Strings
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Issue or Number:10
Record Number:CaltechAUTHORS:20160816-124058470
Persistent URL:
Official Citation:Ciosmak, P., Hadasz, L., Manabe, M. et al. J. High Energ. Phys. (2016) 2016: 44. doi:10.1007/JHEP10(2016)044
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69673
Deposited By: Joy Painter
Deposited On:16 Aug 2016 20:45
Last Modified:11 Nov 2021 04:18

Repository Staff Only: item control page