Transport properties of cascading gauge theories

TL;DR

This work uses gauge/gravity duality to analyze sound propagation in a hot, non-conformal cascading gauge theory plasma at temperatures well above the strong-coupling scale. By constructing a five-dimensional effective gravity theory and studying gauge-invariant fluctuations of a black-brane background, the authors derive the hydrodynamic sound mode from the lowest quasinormal frequency and connect the results to the equation of state. They show that at high temperature the speed of sound deviates from the conformal value as $v_s^2=\tfrac{1}{3}-\tfrac{4}{9}\delta_{cascade}+\cdots$ with $\delta_{cascade}=P^2/K_*$, and obtain a nonzero bulk viscosity $\\zeta$ related to the deviation via $\\\frac{\\zeta}{\\\\eta}=-2\left(v_s^2-\\frac{1}{3}\\right)+O(\\delta_{cascade}^2)$. The dispersion relation includes a cascade-induced correction to both the real and imaginary parts of the sound mode, illustrating how scale generation in the cascading theory manifests in transport coefficients and hydrodynamic behavior relevant to non-conformal plasmas. Overall, the results reinforce and generalize known holographic hydrodynamics for conformal theories to cascading, non-conformal gauge theories with spontaneously generated scales.

Abstract

Cascading gauge theories of Klebanov et.al. provide a model within a framework of gauge theory/string theory duality for a four dimensional non-conformal gauge theory with a spontaneously generated mass scale. Using the dual supergravity description we study sound wave propagation in strongly coupled cascading gauge theory plasma. We analytically compute the speed of sound and the bulk viscosity of cascading gauge theory plasma at a temperature much larger than the strong coupling scale of the theory. The sound wave dispersion relation is obtained from the hydrodynamic pole in the stress-energy tensor two-point correlation function. The speed of sound extracted from the pole of the correlation function agrees with its value computed in [hep-th/0506002] using the equation of state. We find that the bulk viscosity of the hot cascading gauge theory plasma is non-zero at the leading order in the deviation from conformality.