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Thermal correlation functions of KdV charges in 2D CFT.

Maloney, Alexander and Ng, Gim Seng and Ross, Simon F. and Tsiares, Ioannis (2019) 'Thermal correlation functions of KdV charges in 2D CFT.', Journal of high energy physics., 2019 (2). 044.


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.

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Publisher 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.
Date accepted:01 February 2019
Date deposited:20 February 2019
Date of first online publication:07 February 2019
Date first made open access:No date available

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