Relativistic viscous hydrodynamics, conformal invariance, and holography

TL;DR

This paper explores second-order viscous hydrodynamics in conformal field theories, deriving constraints from conformal invariance, matching holographic calculations, and analyzing implications for both strongly and weakly coupled plasmas.

Contribution

It identifies three key second-order transport coefficients in strongly coupled N=4 SYM and highlights missing terms in common hydrodynamic models.

Findings

Conformal invariance constrains second-order hydrodynamics.

Three second-order transport coefficients are determined for N=4 SYM.

Mueller-Israel-Stewart theory omits some conformally required terms.

Abstract

We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled N=4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Mueller-Israel-Stewart theory, often used in numerical simulations, does not contain all allowed second-order terms and, frequently, terms required by conformal invariance.