Elliptic Flow, Kasner Universe and Holographic Dual of RHIC Fireball

TL;DR

The paper addresses modeling RHIC-like fireball expansion using a holographic dual of an anisotropically expanding ${\cal N}=4$ SYM plasma. It extends Bjorken flow to a Kasner-based local rest frame and derives a gravity dual via holographic renormalization, with conformal invariance enforcing Kasner relations. Key results show that the boundary energy density scales as $\rho(\tau)=\frac{\rho_0}{\tau^{4/3}}-\frac{2\eta_0}{\tau^{2}}$, the temperature scales as $T(\tau)=T_0\tau^{-1/3}$, and the entropy approaches a fixed $S_\infty$ determined by microscopic data; the elliptic flow coefficient $v_2$ and eccentricity $\varepsilon$ are computed within the Kasner framework, linking anisotropic expansion to gravity data. The work demonstrates how AdS/CFT can fix macroscopic transport-like quantities from microscopic constants and provides a controlled setting to study anisotropic expansion and elliptic flow in strongly coupled plasmas.

Abstract

We consider a holographic dual of hydrodynamics of N=4 SYM plasma that undergoes non-isotropic three-dimensional expansion relevant to RHIC fireball. Our model is a natural extension of the Bjorken's one-dimensional expansion, and it describes an elliptic flow whose v2 and eccentricity are given in terms of anisotropy parameters. Holographic renormalization shows that absence of conformal anomaly in the SYM theory constrains our local rest frame to be a Kasner spacetime. We show that the Kasner spcetime provides a simple description of the anisotropically expanding fluid within a well-controled approximation. We also find that the dual geometry determines some of the hydrodynamic quantities in terms of the initial condition and the fundamental constants.

Figures (2)

• Figure 1: The available region of $(b,c)$ is on the ellipse between $(0,0)$ and $(1,0)$. $(b,c)=(0,0)$ is Bjorken point
• Figure 2: Time evolution of the elliptic flow parameters. Dotted line is the eccentricity and the solid line is the $v_2$ for $b=0.1$.