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.
Highlights
Introduction and summaryHydrodynamics [1, 2] is the low-energy effective theory for slowly varying fluctuations around thermal equilibrium
We prove analytically that the Haack-Yarom identity H = 2ητπ − 4λ1 − λ2 = 0, which is known to be true for conformal holographic fluids at infinite coupling, holds when taking into account leading non-conformal corrections
The constitutive relations take the form of a systematic expansion in gradients of the fluid variables, gradients which are assumed to be small in the hydrodynamic regime
Summary
Hydrodynamics [1, 2] is the low-energy effective theory for slowly varying fluctuations around thermal equilibrium. Whether H = 0 holds more generally in holographic theories without conformal symmetry remains an open question which we want to address in this paper To this end we compute the second-order transport coefficients entering H for a large class of nonconformal holographic models from three-point functions of the stress tensor. These are four-dimensional holographic theories with a UV fixed point, deformed by a relevant scalar operator of dimension ∆ = 3. Treating the bulk scalar field as a small perturbation, we obtain in subsection 6.1 the leading non-conformal corrections to the transport coefficients in the vicinity of the UV fixed point These leading corrections only depend on the mass term in the scalar potential and apply to all holographic RG flows triggered by a scalar operator of dimension ∆ = 3. We attach technical details of our calculations in appendices A–F
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