Conformal symmetry and non-relativistic second order fluid dynamics

Jingyi Chao; Thomas Schaefer

doi:10.1016/j.aop.2012.02.017

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arXiv · 1108.4979

Conformal symmetry and non-relativistic second order fluid dynamics

Jingyi Chao·Thomas Schaefer

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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.

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Jingyi Chao, Thomas Schaefer. 2011-08-25. Conformal symmetry and non-relativistic second order fluid dynamics. https://doi.org/10.1016/j.aop.2012.02.017

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