Quasi-Normal Modes from Non-Commutative Matrix Dynamics

TL;DR

This paper investigates the relaxation dynamics of the BMN matrix model and its connection to black hole physics in AdS/CFT, focusing on quasi-normal modes and their frequencies through numerical simulations and theoretical comparisons.

Contribution

It introduces a numerical study of quasi-normal modes in the BMN matrix model and compares these with dual gravitational predictions, revealing unexpected similarities.

Findings

Lowest quasi-normal mode frequencies depend on energy

Numerical simulations match gravitational quasi-normal mode frequencies

Surprising similarity between matrix model and AdS black hole modes

Abstract

We explore the connection between the process of relaxation in the BMN matrix model and the physics of black holes in AdS/CFT. Focusing on Dyson-fluid solutions of the matrix model, we perform numerical simulations of the real time dynamics of the system. By quenching the equilibrium distribution we study the quasi-normal oscillations of scalar single trace observables, we isolate the lowest quasi-normal mode, and we determine its frequencies as function of the energy. Considering the BMN matrix model as a truncation of $\mathcal{N}=4$ SYM, we also compute the frequencies of the quasi-normal modes of the dual scalar fields in the AdS$_5$-Schwarzschild background. We compare the results, and we find a surprising similarity.