Ringdown in the SYK model

TL;DR

This work demonstrates that the SYK model at infinite temperature harbors a discrete, quasinormal-mode-like spectrum for thermal correlators, even away from maximal chaos. By combining a high-order perturbative solution of the Schwinger-Dyson equations with a nonperturbative exponential fit, the authors extract resonance frequencies $\omega_n$ and residues $d_n$, revealing a tree-like structure reminiscent of AdS black holes with curvature singularities. A nontrivial bulk-inspired toy model with a curvature singularity reproduces several qualitative features, suggesting a broader holographic intuition beyond the holographic limit. The transition toward large $q$ simplifies the spectrum to imaginary frequencies, while at finite $q$ the spectrum exhibits zeroes and a richly structured pole distribution, raising questions about universality and the bulk interpretation of these resonances.

Abstract

We analyze thermal correlators in the Sachdev-Ye-Kitaev model away from the maximally chaotic limit. Despite the absence of a weakly curved black hole dual, the two point function decomposes into a sum over a discrete set of quasinormal modes. To compute the spectrum of modes, we analytically solve the Schwinger-Dyson equations to a high order in perturbation theory, and then numerically fit to a sum of exponentials using a technique analogous to the double cone construction. The resulting spectrum has a tree-like structure which is reminiscent of AdS black holes with curvature singularities. We present a simple toy model of stringy black holes that qualitatively reproduces some aspects of this structure.

Figures (7)

• Figure 1: Analytic structure of the retarded Green's function at (a) $\lambda=\infty$ and (b) $\lambda=0.$
• Figure 2: The dashed lines mark the discrete sampling times that enter the eigenvalue equation (\ref{['geneig']}) on a grid with $S=5$. The moment expansion gives the correlator up until $t=\beta_0/2$, and the largest time sampled is $t_{\text{max}}<\beta_0/2$.
• Figure 3: The spectrum of resonances in $q=4$ SYK. The magnitude and phase of the residues $d_n$ are indicated by the size and color of the dots, as specified in the legends. The solid dots have converged according to the criterion put forth in the main text, whereas the hollow dots have not yet converged.
• Figure 4:
• Figure 5: The transition from order one $q$ to $q=\infty$. The legends are identical to those in Figure \ref{['qeq4plot']}.