Pole skipping from universal hydrodynamics of (1+1)d QFTs

TL;DR

This paper investigates pole skipping in the stress tensor two-point function of (1+1)d holographic quantum field theories, revealing universal features consistent with hydrodynamic predictions and providing insights into thermalization and chaos.

Contribution

It identifies pole skipping points in holographic QFTs and demonstrates their consistency with universal hydrodynamics and butterfly velocity predictions.

Findings

Pole skipping points are located outside the hydrodynamic regime.

Locations of pole skipping points match resummed hydrodynamic predictions.

Resummation correctly predicts butterfly velocity in holographic theories.

Abstract

(1+1)d QFTs provide a tractable arena for understanding the emergence of hydrodynamics in thermal states. At high temperatures this process is governed by the weak breaking of conformal symmetry, and so in this limit many features of the hydrodynamic theory that emerges have been argued to be universal. In this paper we study aspects of the stress tensor thermal two-point function in holographic QFTs of this kind and show that they are consistent with the universal hydrodynamic theory proposed to apply at late times. Specifically, we identify the locations of the `pole skipping' points in momentum space at which there is an intersection of poles and zeroes of this two-point function in holographic QFTs. Although these points lie outside the regime where the hydrodynamic theory is controlled, we show that their locations are consistent with those found by resumming the hydrodynamic derivative expansion near the lightcone. For example, this resummation of the universal hydrodynamics correctly predicts the butterfly velocity of holographic theories.