Skip to main content

Research Repository

Advanced Search

Thermal correlation functions of KdV charges in 2D CFT

Maloney, Alexander; Ng, Gim Seng; Ross, Simon F.; Tsiares, Ioannis

Thermal correlation functions of KdV charges in 2D CFT Thumbnail


Alexander Maloney

Gim Seng Ng

Ioannis Tsiares


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.


Maloney, A., Ng, G. S., Ross, S. F., & Tsiares, I. (2019). Thermal correlation functions of KdV charges in 2D CFT. Journal of High Energy Physics, 2019(2), Article 44.

Journal Article Type Article
Acceptance Date Feb 1, 2019
Online Publication Date Feb 7, 2019
Publication Date Feb 7, 2019
Deposit Date Feb 20, 2019
Publicly Available Date Feb 20, 2019
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2019
Issue 2
Article Number 44


Published Journal Article (876 Kb)

Publisher Licence URL

Copyright Statement
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.

You might also like

Downloadable Citations