Relativistic dissipative hydrodynamics with spontaneous symmetry breaking

TL;DR

The paper addresses incorporating dissipation into relativistic hydrodynamics for systems with spontaneously broken continuous symmetries, relevant to heavy-ion collisions. It starts from a relativistic superfluid with U(1) breaking and then generalizes to SU(2)_L × SU(2)_R, showing how Goldstone modes enter the hydrodynamic variables and modify the energy-momentum tensor and evolution equations, while dissipation is encoded via fluxes and entropy production. A key contribution is the explicit construction of the energy-momentum tensor with gradient terms from the Goldstone modes and the introduction of a matrix of new transport coefficients that couple baryon, left- and right-chiral currents to the Goldstone sector, subject to positivity and Onsager reciprocity, amounting to 39 independent coefficients. The work highlights potential impacts on heavy-ion observables, proposes deriving Kubo-type relations to compute the coefficients from microscopic theory, and suggests extensions to account for amplitude fluctuations of the order parameter and relaxation-time dynamics for more realistic phenomenology.

Abstract

In this paper we consider dissipative hydrodynamic equations for systems with continuous broken symmetries. We first present the case of superfluidity, in which the symmetry U(1) is broken and then generalize to the chiral symmetry $SU(2)_L \times SU(2)_R$. The corresponding new transport coefficients are introduced.