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From CFT to Ramond super-quantum curves

  • Pawel Ciosmak
  • Leszek Hadasz
  • Zbigniew Jaskólski
  • Masahide Manabe
  • Piotr Sulkowski
Open Access
Regular Article - Theoretical Physics

Abstract

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.

Keywords

Conformal Field Theory Matrix Models 

Notes

Open Access

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.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Pawel Ciosmak
    • 1
  • Leszek Hadasz
    • 2
  • Zbigniew Jaskólski
    • 3
  • Masahide Manabe
    • 4
  • Piotr Sulkowski
    • 5
    • 6
  1. 1.Faculty of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland
  2. 2.M. Smoluchowski Institute of PhysicsJagiellonian UniversityKrakówPoland
  3. 3.Institute of Theoretical PhysicsUniversity of WroclawWroclawPoland
  4. 4.Max-Planck-Institut für MathematikBonnGermany
  5. 5.Faculty of PhysicsUniversity of WarsawWarsawPoland
  6. 6.Walter Burke Institute for Theoretical Physics, California Institute of TechnologyPasadenaU.S.A.

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