Hydrodynamic gradient expansion in gauge theory plasmas

TL;DR

This paper uses gauge/gravity duality to analyze the behavior of hydrodynamic series in gauge theory plasmas, revealing factorial divergence and linking it to nonhydrodynamic modes.

Contribution

It numerically computes high-order hydrodynamic terms and identifies the series divergence and its connection to quasinormal modes in gravity.

Findings

Hydrodynamic series diverges factorially at large orders.

The divergence is linked to the lowest nonhydrodynamic quasinormal mode.

Hydrodynamic gradient expansion has zero radius of convergence.

Abstract

We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives. We observe a factorial growth of gradient contributions at large orders, which indicates a zero radius of convergence of the hydrodynamic series. Furthermore, we identify the leading singularity in the Borel transform of the hydrodynamic energy density with the lowest nonhydrodynamic excitation corresponding to a `nonhydrodynamic' quasinormal mode on the gravity side.