Transport peak in thermal spectral function of ${\cal N}=4$ supersymmetric Yang-Mills plasma at intermediate coupling

Understand

We study the structure of thermal spectral function of the stress-energy tensor in ${\cal N}=4$ supersymmetric Yang-Mills theory at intermediate 't Hooft coupling and infinite number of colors.

• In gauge-string duality, this analysis reduces to the study of classical bulk supergravity with higher-derivative corrections, which correspond to (inverse) coupling corrections on the gauge theory side.
• We extrapolate the analysis of perturbative leading-order corrections to intermediate coupling by non-perturbatively solving the equations of motion of metric fluctuations dual to the stress-energy tensor at zero spatial momentum.
• We observe the emergence of a separation of scales in the analytic structure of the thermal correlator associated with two types of characteristic relaxation modes.