Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

TL;DR

This paper explores the mathematical structure of relativistic hydrodynamics, demonstrating that the hydrodynamic attractor can be derived from divergent gradient expansions using Borel summation and resurgence theory.

Contribution

It introduces a novel approach to understanding hydrodynamic attractors beyond traditional gradient expansion methods, applying resurgence techniques to relativistic viscous hydrodynamics.

Findings

Identification of a universal hydrodynamic attractor

Recovery of the attractor via Borel summation of divergent series

Connection between short-lived modes and resurgence structure

Abstract

Consistent formulations of relativistic viscous hydrodynamics involve short lived modes, leading to asymptotic rather than convergent gradient expansions. In this Letter we consider the Mueller-Israel-Stewart theory applied to a longitudinally expanding quark-gluon plasma system and identify hydrodynamics as a universal attractor without invoking the gradient expansion. We give strong evidence for the existence of this attractor and then show that it can be recovered from the divergent gradient expansion by Borel summation. This requires careful accounting for the short-lived modes which leads to an intricate mathematical structure known from the theory of resurgence.