Conformal symmetry and non-relativistic second order fluid dynamics

TL;DR

This paper explores how conformal symmetry constrains second-order fluid dynamics, revealing specific conditions on the stress tensor, equation of state, and dissipative processes, verified through Boltzmann equation solutions.

Contribution

It provides a detailed analysis of conformal invariance constraints on second-order hydrodynamics, including the stress tensor structure and relaxation dynamics, supported by Boltzmann equation solutions.

Findings

Conformal symmetry enforces a specific equation of state E=2/3 P.

Bulk viscosity must vanish under conformal invariance.

Only a subset of conformally allowed second-order terms appear in the stress tensor.

Abstract

We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P, where E is the energy density and P is the pressure. At first order, conformal symmetry implies that the bulk viscosity must vanish. We show that at second order conformal invariance requires that two-derivative terms in the stress tensor must be traceless, and that it determines the relaxation of dissipative stresses to the Navier-Stokes form. We verify these results by solving the Boltzmann equation at second order in the gradient expansion. We find that only a subset of the terms allowed by conformal symmetry appear.