Thermal correlation functions of KdV charges in 2D CFT

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

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.

Citation

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. https://doi.org/10.1007/jhep02%282019%29044

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2019
• Issue: 2
• Article Number: 44
• DOI: https://doi.org/10.1007/jhep02%282019%29044
• Public URL: https://durham-repository.worktribe.com/output/1307631