From Confinement to Chaos in AdS/CFT Correspondence via Non-equilibrium Local States

TL;DR

The paper investigates non-equilibrium dynamics in AdS/CFT triggered by local operator quenches, first in pure AdS and then in confining geometries created by a hard-wall IR cutoff and capped BTZ black holes. It computes bulk and boundary two-point functions using exact Green’s-function methods and the BDHM dictionary, and analyzes chaos via peak-spacing statistics of boundary observables against random-matrix theory predictions, demonstrating a transition toward Gaussian Symplectic Ensemble behavior for sufficiently heavy operators. In confining AdS, chaos strengthens with larger conformal dimension and with wall proximity, while in capped BTZ, high temperature induces GSE-like statistics even for massless fields, revealing horizon and thermal effects as robust chaos drivers. The results offer holographic benchmarks for chaos in gapped and thermal systems and connect local quenches to universal spectral statistics with potential relevance to lattice and quantum-simulation studies.

Abstract

In this paper, we study excited states in Anti-de Sitter (AdS) space prepared by local operator insertions of a massive scalar field, corresponding to local operator quenches in a free bulk scalar theory. Using the AdS/CFT correspondence, we compute the time evolution of boundary observables in the dual CFT states. We then introduce a hard wall in AdS Poincare coordinates to impose an infrared cutoff (hard-wall), creating a confining deformation of the dual conformal field theory, and analyze the dynamics of excited states in this confining background. By comparing the evolution of boundary two-point correlation functions in the deformed theory to the statistics of Gaussian random matrix ensembles, we show that for sufficiently heavy operators, the spacing-ratio statistics of peaks in temporal dynamics are closest to those of the Gaussian Symplectic Ensemble (GSE). Finally, we extend the analysis to the compact BTZ black hole and to its hard-wall deformation, finding qualitatively similar trends.

Figures (6)

• Figure 1: (a) Bulk dynamics for the condensate $\phi$ for mass parameter corresponding to $\Delta=5$, $m=3.87$ at the moment of time $t=3$ with quench point in the bulk $z_q=1$. (b) Boundary dynamics of $\mathcal{O}^2$ for mass parameter $\Delta=2$, $m=0$ with quench point in the bulk $z_q=0.35$. Parameters $d=2$, $x_q=t_q=0$, $\epsilon=0.1$, $L=1$ are fixed for all figures.
• Figure 2: Bulk dynamics for the condensate $\phi$ for mass parameters corresponding $\nu=1$, $m=0$ (Top) and $\nu=7$, $m=6.93$ (Bottom). Parameters $d=2$, $z_0=2$, $x_q=t_q=0$, $z_q=1.99$, $\epsilon=0.1$, $L=1$, $N=150$ are fixed for all figures, where $N$ is the number of terms taken in the sum over n.
• Figure 3: Boundary dynamics of primary $\mathcal{O}^2$ for different mass parameters at point $x=0$. $d=2$, $z_0=0.2$, $x_q=t_q=0$, $z_q=1.999$, $\epsilon=0.1$, $L=1$, $N=100$ are fixed for all figures.
• Figure 4: Distributions of peak spacing ratios for boundary dynamics of primary $\mathcal{O}^2$ for different mass (massless $\nu=1$ and large mass $\nu=7$) parameters. $d=2$, $z_0=0.2$, $z_q=0.199$, $x_q=t_q=0$, $\epsilon=0.1$, $L=1$, $N=300$ are fixed for all figures.
• Figure 5: Distributions of peak spacing ratios for boundary dynamics of primary $\mathcal{O}^2$ for different mass (massless $\nu=1$ and large mass $\nu=3$) parameters in deformed BTZ geometry. Pannels (a)-(b) correspond to value $r_h=1$ and (c)-(d) -- $r_h=6$ (high temperature regime). Parameters $\varphi_q=t_q=0$, $\epsilon=0.1$, $L=1$, $N=25$, $J_{\text{max}}=40$, $z_0=0.99$, $z_q=0.98$ are fixed for all figures.