Holographic thermalization in N=4 Super Yang-Mills theory at finite coupling

TL;DR

This work analyzes holographic thermalization of a strongly coupled N=4 SYM plasma at finite 't Hooft coupling by combining finite coupling corrections with a collapsing shell model. It tracks how quasinormal modes and spectral densities evolve as the coupling decreases, finding that higher-energy modes become long-lived and deviate more from equilibrium, signaling a weakening of the usual top-down thermalization pattern. The study uses gauge-invariant perturbations in scalar, shear, and sound channels, solving γ-corrected equations of motion and matching across a shell to obtain retarded correlators and the relative spectral density deviation $R_s$. The results corroborate a broader shift toward bottom-up-like behavior at finite coupling and offer insights into non-equilibrium dynamics that are robust to model specifics, while clarifying differences with Vaidya-based approaches and highlighting future directions for fully time-dependent finite-$\lambda$ holography.

Abstract

We investigate the behavior of energy momentum tensor correlators in holographic $\mathcal{N}=4$ super Yang-Mills plasma, taking finite coupling corrections into account. In the thermal limit we determine the flow of quasinormal modes as a function of the 't Hooft coupling. Then we use a specific model of holographic thermalization to study the deviation of the spectral densities from their thermal limit in an out-of-equilibrium situation. The main focus lies on the thermalization pattern with which the plasma constituents approach their thermal distribution as the coupling constant decreases from the infinite coupling limit. All obtained results point towards the weakening of the usual top-down thermalization pattern.

Figures (7)

• Figure 1: The flow of the QNM in the scalar channel for $q=0$ (left) and $q=2\pi T$ (right) as a function of $\lambda$. The dashed lines are drawn to illustrate the bending of the tower of QNM towards the real axis as the coupling constant decreases.
• Figure 2: The flow of the QNM in the shear channel for $q=0$ (left) and $q=2\pi T$ (right).
• Figure 3: The flow of the QNM in the sound channel for $q=0$ (left) and $q=2\pi T$ (right).
• Figure 4: Left: The spectral density for $\lambda=\infty$ in equilibrium (dotted lines) and out of equilibrium for $u_s=0.5$ . Right: The relative deviation of the spectral density for $\lambda=\infty$, $c=8/9,\;5/9,\;0$ (from large to small amplitudes) and $u_s=0.5$ .
• Figure 5: The relative deviation of the spectral density, $R_1$, in the scalar channel, for $c=0$ (dashed black), $c=7/9$ (solid blue), $c=8/9$ (dotted red), with the shell positioned at $u_s=0.5$ and $\lambda=300$ (left), $\lambda=100$ (right).