Hydrodynamic Flow of the Quark-Gluon Plasma and Gauge/Gravity Correspondence

TL;DR

This work surveys how the Gauge/Gravity duality (AdS/CFT) can be used to study the hydrodynamic evolution of the quark‑gluon plasma, focusing on a strongly coupled, conformal gauge theory and its 5D gravity dual. It demonstrates how Bjorken flow emerges from an evolving AdS geometry, with the viscosity bound $\eta/s=1/4\pi$ arising from regularity conditions in the bulk and how hydrodynamic behavior is recovered from a gradient expansion in EF coordinates. It also discusses extensions beyond boost invariance, the resolution of apparent singularities, and explorations of far‑from‑equilibrium dynamics such as shock‑wave collisions, highlighting both the successes and current limitations of the holographic approach for QGP phenomenology.

Abstract

The contribution presents a summary of the Gauge/Gravity approach to the study of hydrodynamic flow of the quark-gluon plasma formed in heavy-ion collisions. Considering the ideal case of a supersymmetric Yang-Mills theory for which the AdS/CFT correspondence gives a precise form of the Gauge/Gravity duality, the properties of the strongly coupled expanding plasma are put in one-to-one correspondence with the metric of a 5-dimensional black hole moving away in the 5th dimension and its deformations consistent with the relevant Einstein equations. Several recently studied aspects of this framework are recalled and put in perspective. This paper is a written version of the four lectures given by the authors on that subject.

Figures (2)

• Figure 1: Description of QGP formation in heavy ion collisions. The kinematic landscape is defined by ${\tau = \sqrt{x_0^2-x_1^2}\ ;\ {\eta=\frac{1}{2} \log \frac{x_0+x_1}{x_0-x_1}}\ ;\ {x_T\!=\!\{x_2,x_3\}}}\ ,$ where the coordinates along the light-cone are $x_0 \pm x_1,$ the transverse ones are $\{x_2,x_3\}$ and $\tau$ is the proper time, $\eta$ the "space-time rapidity".
• Figure 2: In-Out cascade. The "piece of fluid" with space-time rapidity $\eta$ gives rise to hadrons at rapidity $y\equiv\eta,$ after crossing the "freeze-out" hyperbola at fixed proper-time $\tau.$