Generalized Eigenstate Thermalization in 2d CFTs

TL;DR

The paper addresses how large central charge 2d CFTs equilibrate after quenches, showing that the infinite set of local qKdV charges forms a complete thermodynamic description. In the thermodynamic limit, vacuum-block observables are determined by qKdV charge densities, validating a Generalized Gibbs Ensemble (GGE) built from these charges and establishing generalized eigenstate thermalization for these theories. The authors provide explicit expressions up to level 10 for vacuum quasi-primaries in terms of qKdV densities, and analyze GGE realizations with nonnegative chemical potentials as well as two-parameter GGEs, revealing bounds and the necessity of negative chemical potentials in general states. Holographically, equilibration corresponds to black-hole configurations with soft hair, clarifying the role of quantum corrections to classical BTZ gravity and the boundary between primary and generic states. Overall, the work demonstrates that local qKdV charges suffice to describe local equilibrium in large-$c$ 2d CFTs and clarifies the holographic and thermodynamic structure of such equilibria.

Abstract

Infinite-dimensional conformal symmetry in two dimensions leads to integrability of 2d conformal field theories through an infinite tower of local conserved qKdV charges in involution. We discuss the role this integrable structure plays in equilibration of 2d CFTs. We show that in the thermodynamic limit large central charge 2d CFTs satisfy generalized eigenstate thermalization, with the values of qKdV charges forming a complete set of thermodynamically relevant quantities, which unambiguously determine expectation values of all local observables from the vacuum family. Our work settles the question if non-local or quasi-local charges are necessary to describe equilibrium of large central charge 2d CFTs by showing that upon equilibration local physics can be described by the Generalized Gibbs Ensemble that only includes qKdV charges. In the case of a general initial state, upon equilibration, emerging Generalized Gibbs Ensemble will include negative chemical potentials and holographically will be described by a quasi-classical black hole with quantum soft hair.

Figures (1)

• Figure 1: Plot of $q_{2k-1}/q_1^k-1$ in the units of $1/c$ as a function of $\tau=\beta(\pi^2/(6c\mu_3))^{1/3}$ for $k=2,3$. It approaches zero as $|\tau|^{-3}$ for all $k$ when $\tau\rightarrow -\infty$. The opposite limit $\tau\rightarrow \infty$ corresponds to the Gibbs ensemble, $q_1\sim \beta^{-1}$, $\mu_3\rightarrow 0$, and $c(q_{2k-1}/q_1^k-1)$ for $k=2,3$ approach $22/5$ and $302/21$ correspondingly.