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

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