A Novel Formula for Bulk Viscosity from the Null Horizon Focusing Equation

TL;DR

The paper derives a compact holographic formula for bulk viscosity, relating $\zeta/\eta$ to horizon data via $\frac{\zeta}{\eta} = \sum_i \left( s \frac{d \phi^{H}_i}{ds} + \rho^a \frac{d \phi^{H}_i}{d \rho^a} \right)^2$, and shows how the flux of horizon scalar fields governs bulk dissipation. By mapping the Raychaudhuri equation to the fluid entropy balance, the authors connect horizon geometry to boundary hydrodynamics in both conformal and non-conformal theories. The formula is validated across non-conformal branes, deformations of $\mathcal{N}=4$ SYM, and holographic QCD models, reproducing known results and providing analytic expressions in several cases. The work also discusses regimes of applicability (high temperature, adiabatic limits) and highlights limitations related to IR/UV running and frame choices in Kubo comparisons. Overall, it offers a unifying horizon-based method to compute bulk viscosity in strongly coupled holographic plasmas with scalar hair.

Abstract

The null horizon focusing equation is equivalent via the fluid/gravity correspondence to the entropy balance law of the fluid. Using this equation we derive a simple novel formula for the bulk viscosity of the fluid. The formula is expressed in terms of the dependence of scalar fields at the horizon on thermodynamic variables such as the entropy and charge densities. We apply the formula to three classes of gauge theory plasmas: non-conformal branes, perturbations of the N=4 supersymmetric Yang-Mills theory and holographic models of QCD, and discuss its range of applicability.