Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit

TL;DR

This work analyzes the Generalized Gibbs Ensemble for 2d CFTs decorated with higher qKdV charges in the thermodynamic limit, deriving the extensive free energy and organizing leading $1/c$ corrections as sums over Young tableaux. It shows that at infinite central charge the GGE and the eigenstate ensemble agree at the level of local observables for any fugacities, aligning with holographic expectations, but at finite $c$ they differ due to nontrivial contributions from the subleading parts of qKdV charges. The authors provide explicit results for the first two charges, $Q_3$ and $Q_5$, including integral representations and perturbative expansions in the rescaled fugacities $t_{2k-1}$, and they argue that primary states cannot be tuned to reproduce the GGE at finite $c$. Overall, the paper exposes a nuanced picture of thermalization and ETH in 2d CFTs, highlighting the role of integrable structure and its impact on holographic interpretations. It suggests directions for further study of higher-order $1/c$ effects and the behavior of non-vacuum blocks in the GGE framework.

Abstract

We discuss partition function of 2d CFTs decorated by higher qKdV charges in the thermodynamic limit when the size of the spatial circle goes to infinity. In this limit the saddle point approximation is exact and at infinite central charge generalized partition function can be calculated explicitly. We show that leading 1/c corrections to free energy can be reformulated as a sum over Young tableaux which we calculate for the first two qKdV charges. Next, we compare generalized ensemble with the "eigenstate ensemble" that consists of a single primary state. At infinite central charge the ensembles match at the level of expectation values of local operators for any values of qKdV fugacities. When the central charge is large but finite, for any values of the fugacities the aforementioned ensembles are distinguishable.