Thermal spectral functions of strongly coupled N=4 supersymmetric Yang-Mills theory

TL;DR

This work uses gauge-gravity duality to compute non-perturbative, finite-temperature spectral functions of the stress-energy tensor in ${\cal N}=4$ SYM at large ${N_c}$ and large ${\rm \lambda}$. By solving boundary-value problems for linear perturbations in the AdS-Schwarzschild background, it obtains the retarded correlators in the three symmetry channels and derives the full spectral functions, revealing hydrodynamic peaks at low frequency and damped oscillations at intermediate frequencies that differ from perturbative expectations. The study confirms ${\eta}/{s}=1/{4\pi}$ and shows how the finite-temperature spectral functions approach their zero-temperature forms at high frequency, offering insights for lattice extractions of transport coefficients in thermal gauge theories. These results provide a non-perturbative benchmark for real-time dynamics in strongly coupled gauge theories and a potential input for improving lattice spectral reconstructions.

Abstract

We use the gauge-gravity duality conjecture to compute spectral functions of the stress-energy tensor in finite temperature N=4 supersymmetric Yang-Mills theory in the limit of large Nc and large coupling. The spectral functions exhibit peaks characteristic of hydrodynamic modes at small frequency, and oscillations at intermediate frequency. The non-perturbative spectral functions differ qualitatively from those obtained in perturbation theory. The results may prove useful for lattice studies of transport processes in thermal gauge theories.

Figures (2)

• Figure 1: Finite-temperature part of the spectral function for transverse stress $(\chi_{xy,xy}-\chi_{xy,xy}^{T=0})/{\textswab{w}}$, plotted in units of $\pi^2N_{\rm c}^2 T^4$ as a function of dimensionless frequency ${\textswab{w}}\equiv\omega/2\pi T$. Different curves correspond to values of the dimensionless spatial momentum ${\textswab{q}}\equiv q/2\pi T$ equal to $0$, $0.6$, $1.0$, and $1.5$.
• Figure 2: Left: spectral function for longitudinal momentum density, $\chi_{tx,tx}$, plotted in units of $\pi^2N_{\rm c}^2 T^4$, as a function of dimensionless frequency ${\textswab{w}}\equiv\omega/2\pi T$. Different curves correspond to values of the dimensionless spatial momentum ${\textswab{q}}\equiv q/2\pi T$ equal to $0.3$, $0.6$, $1.0$, and $1.5$. At large ${\textswab{w}}$, the curves asymptote to the zero-temperature result $\frac{\pi}{2} {\textswab{q}}^2 ({\textswab{w}}^2-{\textswab{q}}^2)$. Right: spectral function for energy density, $\chi_{tt,tt}$, plotted in units of $\pi^2N_{\rm c}^2 T^4$, as a function of dimensionless frequency ${\textswab{w}}\equiv\omega/2\pi T$. Different curves correspond to values of the dimensionless spatial momentum ${\textswab{q}}\equiv q/2\pi T$ equal to $0.3$, $0.6$, $1.0$, and $1.5$. At large ${\textswab{w}}$, the curves asymptote to the zero-temperature result $\frac{\pi}{2}\, 4{\textswab{q}}^4/3$.