Density Dependence of Transport Coefficients from Holographic Hydrodynamics

TL;DR

Ge, Matsuo, Shu, Sin, and Tsukioka study transport coefficients of a holographic quark-gluon plasma at finite temperature and finite baryon density using RN–AdS5 with bulk U(1) filling branes. They perturb the RN–AdS background, derive vector and tensor master equations, and extract $D=\frac{b}{2(1+a)}$ for diffusion and confirm the universal ratio $\frac{\eta}{s}=\frac{1}{4\pi}$. They show that $D$ and the thermodynamic quantities satisfy $D=\frac{\eta}{\varepsilon+p}$ and compute the thermal conductivity via Kubo relations, obtaining $\kappa_T= -\frac{(\varepsilon+p)^2}{\rho^2 T}\lim_{\omega\to0}\frac{\mathrm{Im}(G(\omega,0))}{\omega}=2\pi^2\frac{N_c}{N_f}\frac{\eta T}{\mu^2}$. The density dependence reveals diffusion and viscosity decrease with charge at fixed energy, while for fixed temperature the fluid thickens with increasing baryon density, offering insights into baryon-rich QGP and supporting universality of holographic transport.

Abstract

We study the transport coefficients of Quark-Gluon-Plasma in finite temperature and finite baryon density. We use AdS/QCD of charged AdS black hole background with bulk-filling branes identifying the U(1) charge as the baryon number. We calculate the diffusion constant, the shear viscosity and the thermal conductivity to plot their density and temperature dependences. Hydrodynamic relations between those are shown to hold exactly. The diffusion constant and the shear viscosity are decreasing as a function of density for fixed total energy. For fixed temperature, the fluid becomes less diffusible and more viscous for larger baryon density.

Figures (6)

• Figure 1: $D$ vs. $q$ and $m$ ($l=1$)
• Figure 2: $D$ vs. $q$ and $T$$(l=1)$
• Figure 3: $\eta$ vs. $q$ and $m$ ($\kappa=l=1$)
• Figure 4: $\eta$ vs. $q$ and $T$$(\kappa=l=1)$
• Figure 5: $\kappa_T$ vs. $q$ and $m$ ($\kappa=l=1$)