Shear Modes, Criticality and Extremal Black Holes

TL;DR

This paper investigates the low-frequency behavior of retarded correlators in a holographic (2+1)-dimensional field theory dual to an extremal Reissner-Nordstrom AdS(4) black hole, revealing emergent scaling and the spectral structure of quasinormal modes.

Contribution

It provides a detailed numerical analysis of electromagnetic and gravitational quasinormal modes at extremality, uncovering the spectral structure and emergent scaling in the dual field theory.

Findings

Correlators exhibit emergent low-frequency scaling behavior.

Spectral poles form a branch cut and isolated damped excitations.

All poles are in the lower half-plane, indicating stability.

Abstract

We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential fixed.