Hydrodynamics of Sakai-Sugimoto model in the quenched approximation

TL;DR

The authors analyze transport properties in the finite-temperature Sakai–Sugimoto model within the quenched (probe) approximation, focusing on the sound mode of the deconfined phase. They derive a consistent five-dimensional effective action via KK reduction on $S^1\times S^4$, establish the background black-brane geometry, and compute thermodynamics to obtain the speed of sound $v_s$ in the plasma. By studying fluctuations and constructing gauge-invariant variables, they solve the hydrodynamic equations to extract the sound dispersion, obtaining $v_s = 1/\sqrt{5}$ and $\zeta/\eta = 4/15$, with attenuation characterized by $\Gamma = 2/5$ in appropriate units. The results show no imprint of the first-order confinement/deconfinement transition on the transport properties, highlighting the decoupling between thermodynamics of the phase transition and hydrodynamic transport in this holographic model.

Abstract

We study transport properties of the finite temperature Sakai-Sugimoto model. The model represents a holographic dual to 4+1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks localized at different points on the compact circle. We analytically compute the speed of sound and the sound wave attenuation in the quenched approximation. Since confinement/deconfinement (and the chiral symmetry restoration) phase transitions are first order in this model, we do not see any signature of these phase transitions in the transport properties.