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

TL;DR

This paper investigates second-order hydrodynamic transport in non-conformal holographic fluids, deriving new formulas, analyzing specific RG flows, and providing evidence that a known universal identity holds beyond conformal cases.

Contribution

The authors derive new Kubo formulas for second-order transport coefficients and demonstrate the universality of the Haack-Yarom identity in non-conformal holographic fluids.

Findings

Explicit expressions for five second-order transport coefficients at infinite coupling.

The identity $ ilde{H}=0$ holds universally in studied models.

The Haack-Yarom identity $H=0$ persists beyond conformal 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, $\tilde{H}=2\eta\tau_\pi-2(\kappa-\kappa^*)-\lambda_2$, 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.