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Journal of High Energy Physics

, 2019:44 | Cite as

Thermal correlation functions of KdV charges in 2D CFT

  • Alexander Maloney
  • Gim Seng Ng
  • Simon F. RossEmail author
  • Ioannis Tsiares
Open Access
Regular Article - Theoretical Physics
  • 11 Downloads

Abstract

Two dimensional CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges, built out of the stress tensor. We compute the thermal correlation functions of the these KdV charges on a circle. We show that these correlation functions are given by quasi-modular differential operators acting on the torus partition function. We determine their modular transformation properties, give explicit expressions in a number of cases, and give an expression for an arbitrary correlation function which is determined up to a finite number of functions of the central charge. We show that these modular differential operators annihilate the characters of the (2m + 1, 2) family of non-unitary minimal models. We also show that the distribution of KdV charges becomes sharply peaked at large level.

Keywords

Conformal Field Theory Integrable Hierarchies 

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) 2019

Authors and Affiliations

  • Alexander Maloney
    • 1
  • Gim Seng Ng
    • 2
    • 3
  • Simon F. Ross
    • 4
    Email author
  • Ioannis Tsiares
    • 1
  1. 1.Department of PhysicsMcGill UniversityMontréalCanada
  2. 2.School of MathematicsTrinity College DublinDublin D2Ireland
  3. 3.Hamilton Mathematical InstituteTrinity College DublinDublin D2Ireland
  4. 4.Centre for Particle Theory, Department of Mathematical SciencesDurham UniversityDurhamU.K.

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