Generalized Gibbs Ensemble and the Statistics of KdV Charges in 2D CFT

TL;DR

This paper investigates the statistical properties of quantum KdV charges in 2D conformal field theories, analyzing the Generalized Gibbs Ensemble at high temperature and finite central charge, revealing degeneracy and sharp peaking behaviors.

Contribution

It provides a detailed analysis of the GGE in 2D CFTs, including the effects of finite central charge and the statistical distribution of KdV charges.

Findings

GGE values match microstate values at high temperature and large central charge.

Degeneracy of KdV charges is broken at finite central charge.

KdV charges are sharply peaked at high level within a Virasoro representation.

Abstract

Two-dimensional CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges. We study the Generalized Gibbs Ensemble with chemical potentials for these charges at high temperature. In a large central charge limit, the partition function can be computed in a saddle-point approximation. We compare the ensemble values of the KdV charges to the values in a microstate, and find that they match irrespective of the values of the chemical potentials. We study the partition function at finite central charge perturbatively in the chemical potentials, and find that this degeneracy is broken. We also study the statistics of the KdV charges at high level within a Virasoro representation, and find that they are sharply peaked.