Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence

TL;DR

This paper investigates the GGE of 2D CFTs with U(1) charge using the AGT correspondence, analyzing the partition function and eigenstate thermalization in the semiclassical limit and with quantum corrections.

Contribution

It introduces a novel approach to compute the GGE partition function of charged 2D CFTs via AGT and explores the large central charge limit and quantum corrections.

Findings

GGE averages match primary eigenvalues at large c limit

Finite c partition function expressed with partial theta functions

Potential violation of eigenstate thermalization at subleading 1/c order

Abstract

The Generalized Gibbs Ensemble (GGE) is relevant to understand the thermalization of quantum systems with an infinite set of conserved charges. In this work, we analyze the GGE partition function of 2D Conformal Field Theories (CFTs) with a U(1) charge and quantum Benjamin-Ono$_{2}$ (qBO$_{2}$) hierarchy charges. We use the Alday-Gaiotto-Tachikawa (AGT) correspondence to express the thermal trace in terms of the Alba-Fateev-Litvinov-Tarnopolskiy (AFLT) basis of descendants, which diagonalizes all charges. We analyze the GGE partition function in the thermodynamic semiclassical limit, including the first order quantum correction. We find that the equality between GGE averages and primary eigenvalues of the qBO$_{2}$ charges is attainable in the strict large $c$ limit and potentially violated at the subleading $1/c$ order. We also obtain the finite $c$ partition function when only the first non-trivial charge is turned on, expressed in terms of partial theta functions. Our results should be relevant to the eigenstate thermalization hypothesis for charged CFTs, Warped CFTs and effective field theory descriptions of condensed matter systems.