AdS/CFT correspondence, quasinormal modes, and thermal correlators in N=4 SYM

TL;DR

This paper employs the AdS/CFT correspondence to analyze quasinormal modes and thermal correlators in N=4 SYM theory, providing new definitions, formulas, and connections to hydrodynamics at finite temperature.

Contribution

It introduces a natural definition for quasinormal modes in asymptotically AdS spacetimes and derives explicit formulas for their frequencies in various perturbation cases.

Findings

Derived asymptotic formulas for scalar and tensor quasinormal frequencies.

Obtained an exact expression for vector perturbation frequencies.

Connected quasinormal modes to hydrodynamic behavior in thermal gauge theory.

Abstract

We use the Lorentzian AdS/CFT prescription to find the poles of the retarded thermal Green's functions of ${\cal N=4}$ SU(N) SYM theory in the limit of large N and large 't Hooft coupling. In the process, we propose a natural definition for quasinormal modes in an asymptotically AdS spacetime, with boundary conditions dictated by the AdS/CFT correspondence. The corresponding frequencies determine the dispersion laws for the quasiparticle excitations in the dual finite-temperature gauge theory. Correlation functions of operators dual to massive scalar, vector and gravitational perturbations in a five-dimensional AdS-Schwarzschild background are considered. We find asymptotic formulas for quasinormal frequencies in the massive scalar and tensor cases, and an exact expression for vector perturbations. In the long-distance, low-frequency limit we recover results of the hydrodynamic approximation to thermal Yang-Mills theory.