Holography and the speed of sound at high temperatures

TL;DR

This paper shows that in a broad class of holographic models with a single scalar field encoding scale violation, the speed of sound $c_s^2$ universally approaches the conformal value $1/3$ from below at high temperature. Using a 5D gravity–scalar setup with action $S_5$ and a scalar potential $V(\phi)$, the authors relate $\epsilon$, $p$, and the trace anomaly $\theta=\epsilon-3p$ to the enthalpy $w=\epsilon+p$ and derive an exact expression for $c_s^2$ in terms of $d\theta/dw$. In the high-$T$ limit, they obtain an analytic correction $c_s^2 = 1/3 - \frac{1}{9} c^2 \Delta_- (\Delta_+-\Delta_-)^2 w^{-\Delta_-/2} D(\Delta_-) + \ldots$, with a negative sign and a coefficient determined by near-origin data $V''(0)=m^2$, reflecting universality controlled by the operator responsible for the scale anomaly. The results tie to horizon data and scale-anomaly susceptibilities, align with lattice QCD trends at $T\gg \Lambda_{QCD}$, and provide a holographic explanation for the approach to conformality from below in strongly coupled thermal plasmas.

Abstract

We show that in a general class of strongly interacting theories at high temperatures the speed of sound approaches the conformal value c_s^2=1/3 universally from_below_. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly.