New theories of relativistic hydrodynamics in the LHC era

TL;DR

This paper reviews recent theoretical advances in relativistic hydrodynamics relevant to heavy-ion collisions at RHIC and LHC, emphasizing microscopic physics, hydrodynamization, and mathematical models.

Contribution

It provides a unified overview of the field with new insights into the large-order behaviour of the hydrodynamic gradient expansion.

Findings

Discussion of the gradient expansion and hydrodynamization phenomena

Introduction of new results on the large-order behaviour of the gradient expansion

Analysis of models of hydrodynamic evolution equations

Abstract

The success of relativistic hydrodynamics as an essential part of the phenomenological description of heavy-ion collisions at RHIC and the LHC has motivated a significant body of theoretical work concerning its fundamental aspects. Our review presents these developments from the perspective of the underlying microscopic physics, using the language of quantum field theory, relativistic kinetic theory, and holography. We discuss the gradient expansion, the phenomenon of hydrodynamization, as well as several models of hydrodynamic evolution equations, highlighting the interplay between collective long-lived and transient modes in relativistic matter. Our aim to provide a unified presentation of this vast subject -- which is naturally expressed in diverse mathematical languages -- has also led us to include several new results on the large-order behaviour of the hydrodynamic gradient~expansion.