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

TL;DR

This paper investigates the thermal spectral function of the stress-energy tensor in ${\cal N}=4$ supersymmetric Yang-Mills theory at intermediate coupling, revealing a transport peak indicative of quasiparticle-like behavior through holographic methods.

Contribution

It provides a non-perturbative analysis of the spectral function at intermediate coupling using gauge-string duality with higher-derivative corrections, highlighting a transport peak structure.

Findings

Identification of a narrow transport peak in the spectral function.

Evidence of a separation of relaxation scales in the correlator.

Comparison with perturbative expectations suggests quasiparticle-like excitations.

Abstract

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. As a consequence of this separation, the associated spectral function exhibits a narrow structure in the small frequency region which controls the dynamics of transport in the theory and may be described as a transport peak typically found in perturbative, weakly interacting thermal field theories. We compare our results with generic expectations drawn from perturbation theory, where such a structure emerges as a consequence of the existence of quasiparticles.