On Eling-Oz formula for the holographic bulk viscosity

TL;DR

This paper examines the Eling-Oz formula for holographic bulk viscosity, confirming its accuracy across different plasma models and near critical points, thus validating its broad applicability.

Contribution

The paper demonstrates that the Eling-Oz formula accurately predicts bulk viscosity in cascading and N=2* plasmas, including near critical points, extending its validated regime.

Findings

The formula agrees with previous calculations for cascading plasma.

It correctly reproduces critical behavior near phase transitions.

Validates the formula's applicability beyond high-temperature regimes.

Abstract

Recently Eling and Oz [1] proposed a simple formula for the bulk viscosity of holographic plasma. They argued that the formula is valid in the high temperature (near-conformal) regime, but is expected to break down at low temperatures. We point out that the formula is in perfect agreement with the previous computations of the bulk viscosity of the cascading plasma [2,3], as well as with the previous computations of the bulk viscosity of N=2^* plasma [4,5]. In the latter case it correctly reproduces the critical behaviour of the bulk viscosity in the vicinity of the critical point with the vanishing speed of sound.