Finite Temperature Spectral Densities of Momentum and R-Charge Correlators in $\N=4$ Yang Mills Theory

TL;DR

This paper addresses the non-perturbative transport properties of a strongly coupled plasma by computing finite-temperature spectral densities of momentum and R-charge correlators in $\mathcal{N}=4$ SYM using AdS/CFT. It derives hydrodynamic limits for stress-tensor and R-charge correlators and computes the full frequency dependence, showing that at strong coupling there is no kinetic- theory peak at $\omega\sim T$, while at large $\omega$ the densities approach the zero-temperature results with exponential damping. The Euclidean correlators are surprisingly close to the free theory (about $10\%$–$20\%$), implying that lattice QCD transport coefficients may be difficult to extract from Euclidean data alone. The work provides quantitative benchmarks for interpreting lattice results and contrasts strong-coupling dynamics with perturbative/QCD expectations, informing our understanding of transport in strongly interacting plasmas. Key results include $\eta/(e+p)=1/(4\pi T)$, $D=1/(2\pi T)$, and detailed spectral densities in both the stress-energy and R-charge channels.

Abstract

We compute spectral densities of momentum and R-charge correlators in thermal $\N=4$ Yang Mills at strong coupling using the AdS/CFT correspondence. For $ω\sim T$ and smaller, the spectral density differs markedly from perturbation theory; there is no kinetic theory peak. For large $ω$, the spectral density oscillates around the zero-temperature result with an exponentially decreasing amplitude. Contrast this with QCD where the spectral density of the current-current correlator approaches the zero temperature result like $(T/ω)^4$. Despite these marked differences with perturbation theory, in Euclidean space-time the correlators differ by only $\sim 10%$ from the free result. The implications for Lattice QCD measurements of transport are discussed.

Figures (3)

• Figure 1: (a) The spectral density of the stress energy tensor, $\pi \rho_{\tau\tau}^{yxyx}(\omega)/\omega$ normalized by the shear viscosity, $\eta_{ AdS} = \pi N^2 T^3/8$. (b) The spectral density of the current-current correlator, $\pi \rho_{JJ}/\omega$ normalized by $\chi_s D = N^2 T^2/16\pi T$. In both cases the dashed curves show the zero temperature results (Eq. (\ref{['rho_tau_0T']}) and Eq. (\ref{['rho_j_0T']})) normalized by the same factors. Due to a non-renormalization theorem in these channels, the zero temperature spectral densities in the free and interacting theories are equal Freedman:1998tzChalmers:1998xr. At finite temperature the kinetic theory peak does not exist in the strongly interacting theory.
• Figure 2: The spectral density of the (a) stress energy tensor and (b) current-current correlators as in Fig. \ref{['rho']} but the zero temperature result has been subtracted and the absolute value taken. The plus or minus indicates the sign. The finite temperature spectral densities oscillate around the zero temperature result with exponentially decreasing amplitude.
• Figure 3: The Euclidean correlator for the (a) stress energy tensor correlator, $G^{yxyx}_{\tau\tau}$, and the (b) current-current correlator, $G_{JJ}$. The dashed curves show the free result for these Euclidean correlators.