Universal thermalization dynamics in (1+1)d QFTs

TL;DR

This paper uncovers a universal mechanism for thermalization in (1+1)d quantum field theories, linking conformal perturbation theory breakdown to hydrodynamics emergence and providing universal expressions for transport parameters.

Contribution

It demonstrates the universal breakdown of conformal perturbation theory leading to hydrodynamics and derives universal transport parameters for theories with large central charge.

Findings

Hydrodynamics emerges universally due to stress tensor exchange near the lightcone.

Conformal perturbation theory breaks down at late times, enabling hydrodynamics.

Transport parameters have universal expressions in terms of the perturbation's scaling dimension.

Abstract

We identify the universal mechanism behind the thermalization of (1+1)d QFTs at high and low temperatures. Viewing these theories as CFTs perturbed by relevant or irrelevant deformations, we show that conformal perturbation theory in the thermal state breaks down at late times allowing for the emergence of hydrodynamics. This breakdown occurs universally due to the unsuppressed exchange of stress tensors near the lightcone. Furthermore, for theories with central charge $c\rightarrow\infty$ we solve for the emergent hydrodynamic theory to all orders in the gradient expansion by arguing that all transport parameters appearing in two-point functions have universal expressions in terms of the scaling dimension $\Delta$ of the perturbation. The radius of convergence of the hydrodynamic dispersion relations provides an early time cutoff for hydrodynamics, which agrees with the time scale at which conformal perturbation theory breaks down.