Resolving disagreement for eta/s in a CFT plasma at finite coupling

TL;DR

Problem: resolve the previously reported discrepancy in the finite-coupling correction to $\eta/s$ between equilibrium CFT calculations and the Janik-Peschanski holographic dual. Approach: analyze horizon boundary conditions for metric fluctuations at ${\cal O}(\alpha'^3)$ and show that the incoming-wave condition must be applied on the corrected background, then compute corrected quasinormal modes in the hydrodynamic limit. Findings: corrected boundary condition yields $\eta/s = \frac{1}{4\pi}\left(1 + 15\zeta(3)\lambda^{-3/2} + \cdots\right)$, agreeing with the JP prediction; QNM frequencies acquire ${\cal O}(\gamma)$ shifts (e.g., $\mathfrak{w} = -i \mathfrak{q}^2(1/2 + 105\gamma/2) + \cdots$ for shear and $\mathfrak{w} = (1/\sqrt{3})\mathfrak{q} - i \mathfrak{q}^2(1/3 + 105\gamma/3) + \cdots$ for sound). Conformal symmetry forbids ${\cal O}(\gamma)$ corrections to the speed of sound and bulk viscosity. Significance: resolves the previous mismatch and reinforces the universality of holographic transport at finite coupling, clarifying boundary-condition treatment in higher-derivative holography.

Abstract

The ratio of shear viscosity to entropy density in a strongly coupled CFT plasma can be computed using the AdS/CFT correspondence either from equilibrium correlation functions or from the Janik-Peschanski dual of the boost invariant plasma expansion. We point out that the previously found disagreement for eta/s at finite t' Hooft coupling is resolved once the incoming-wave boundary condition for metric fluctuations at the horizon of the dual geometry is properly imposed.