Thermalization with chemical potentials, and higher spin black holes

TL;DR

This paper investigates how local observables in 1+1D conformal field theories with conserved charges relax to equilibrium after a quantum quench, linking thermalization rates to higher spin black hole quasinormal modes.

Contribution

It introduces a new technique to compute thermalization rates and relaxation times in CFTs with multiple chemical potentials, connecting these results to higher spin holography.

Findings

Exponential approach of local observables to equilibrium values.

Systematic perturbation method for chemical potentials.

Agreement of thermalization rates with higher spin black hole quasinormal frequencies.

Abstract

We study the long time behaviour of local observables following a quantum quench in 1+1 dimensional conformal field theories possessing additional conserved charges besides the energy. We show that the expectation value of an arbitrary string of {\it local} observables supported on a finite interval exponentially approaches an equilibrium value. The equilibrium is characterized by a temperature and chemical potentials defined in terms of the quenched state. For an infinite number of commuting conserved charges, the equilibrium ensemble is a generalized Gibbs ensemble (GGE). We compute the thermalization rate in a systematic perturbation in the chemical potentials, using a new technique to sum over an infinite number of Feynman diagrams. The above technique also allows us to compute relaxation times for thermal Green's functions in the presence of an arbitrary number of chemical potentials. In the context of a higher spin (hs[\lambda]) holography, the partition function of the final equilibrium GGE is known to agree with that of a higher spin black hole. The thermalization rate from the CFT computed in our paper agrees with the quasinormal frequency of a scalar field in this black hole.