Second-Order Hydrodynamics and Universality in Non-Conformal Holographic Fluids

Abstract

We study second-order hydrodynamic transport in strongly coupled non-conformal field theories with holographic gravity duals in asymptotically anti-de Sitter space. We first derive new Kubo formulae for five second-order transport coefficients in non-conformal fluids in $(3+1)$ dimensions. We then apply them to holographic RG flows induced by scalar operators of dimension $\Delta =3$. For general background solutions of the dual bulk geometry, we find explicit expressions for the five transport coefficients at infinite coupling and show that a specific combination, $\tilde{H}=2\eta {\tau }_{\pi }-2(\kappa -{\kappa }^{\ast })-{\lambda }_2$, always vanishes. We prove analytically that the Haack-Yarom identity $H=2\eta {\tau }_{\pi }-4{\lambda }_1-{\lambda }_2=0$, which is known to be true for conformal holographic fluids, also holds when taking into account leading non-conformal corrections. The numerical results we obtain for two specific families of RG flows suggest that $H$ vanishes regardless of conformal symmetry. Our work provides further evidence that the Haack-Yarom identity $H=0$ may be universally satisfied by strongly coupled fluids.

arXiv comment33 pages + 6 appendices, 5 figures; v2 as published in JHEP

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