# Holography of the QGP Reynolds Number

## TL;DR

This paper explores holographic models of the Quark-Gluon Plasma, focusing on the Reynolds number and kinematic viscosity, revealing bounds and dependencies on magnetic fields and impact parameters.

## Contribution

It introduces a holographic approach to analyze the Reynolds number and kinematic viscosity of QGP, highlighting their variability and bounds in relation to physical parameters.

## Key findings

- Upper bound on Reynolds number for central collisions matches observations.
- Kinematic viscosity and Reynolds number vary with magnetic field and impact parameter.
- In Einstein gravity holography, η/s remains constant while ν and Re vary.

## Abstract

The viscosity of the Quark-Gluon Plasma (QGP) is usually described holographically by the entropy-normalized dynamic viscosity $\eta/s$. However, other measures of viscosity, such as the kinematic viscosity $\nu$ and the Reynolds number $Re$, are often useful, and they too should be investigated from a holographic point of view. We show that a simple model of this kind puts an upper bound on $Re$ for nearly central collisions at a given temperature; this upper bound is in very good agreement with the observational lower bound (from the RHIC facility). Furthermore, in a holographic approach using only Einstein gravity, $\eta/s$ does not respond to variations of other physical parameters, while $\nu$ and $Re$ can do so. In particular, it is known that the magnetic fields arising in peripheral heavy-ion collisions vary strongly with the impact parameter $b$, and we find that the holographic model predicts that $\nu$ and $Re$ can also be expected to vary substantially with the magnetic field and therefore with $b$.