Residues of Correlators in the Strongly Coupled N=4 Plasma

TL;DR

This paper calculates the residues of quasinormal modes in the strongly coupled N=4 plasma, revealing their complex nature and behavior with momentum, which helps define the hydrodynamic regime's onset time.

Contribution

It provides the first detailed computation of residues for R-charge current quasinormal modes in the AdS/CFT context, enhancing understanding of the plasma's response.

Findings

Residues are complex except for the hydrodynamic mode.

Residue magnitude increases with momentum q.

Hydrodynamic mode residues are purely imaginary and exhibit zeroes at finite q.

Abstract

Quasinormal modes of asymptotically AdS black holes can be interpreted as poles of retarded correlators in the dual gauge theory. To determine the response of the system to small external perturbations it is not enough to know the location of the poles: one also needs to know the residues. We compute them for R-charge currents and find that they are complex except for the hydrodynamic mode, whose residue is purely imaginary. For different quasinormal modes the residue grows with momentum q, whereas for the hydrodynamic mode it behaves as a damped oscillation with distinct zeroes at finite q. Similar to collective excitations at weak coupling the hydrodynamic mode decouples at short wavelengths. Knowledge of the residues allows as well to define the time scale t_H from when on the system enters the hydrodynamic regime, restricting the validity of hydrodynamic simulations to times t>t_H.