Analytic long-lived modes in charged critical plasma

TL;DR

This paper investigates the quasi-normal modes of charged holographic plasmas near criticality, revealing distinct mode sets, their behavior in extremal limits, and developing analytical and numerical methods applicable to Lifshitz black branes.

Contribution

It introduces an analytical approach to study quasi-normal modes in charged critical plasmas using 2D black hole reflection amplitudes and develops a WKB method for Lifshitz geometries.

Findings

Identified decoupled and non-decoupled mode sets with distinct behaviors.

Observed branch cut formation signaling hydrodynamic breakdown.

Extended analysis to Lifshitz black branes using WKB approximation.

Abstract

Fluctuations around critical behavior of a holographic charged plasmas are investigated by studying quasi-normal modes of the corresponding black branes in 5D Einstein-Maxwell-Dilaton gravity. The near horizon geometry of black branes approaches the well-known 2D charged string black hole in the critical limit, for which a world-sheet description is available, and the corresponding quasi-normal modes can be obtained analytically from the reflection amplitude of the 2D black hole geometry. We find two distinct set of modes: a purely imaginary ``decoupled'' set, directly following from the reflection amplitude, and a ``non-decoupled'' set that was already identified in the neutral holographic plasma in \cite{Betzios:2018kwn}. In the extremal limit, the former set of imaginary quasi-normal modes coalesce on a branch cut starting from the the origin, signaling breakdown of hydrodynamic approximation. We further complete the black brane geometry with a slice of AdS near the boundary, to allow for a holographic construction, and find another set of modes localized in the UV. Finally, we develop an alternative WKB method to obtain the quasi-normal modes in the critical limit and apply this method to study the spectrum of hyperscaling-violating Lifshitz black branes. The critical limit of the plasma we consider in this paper is in one-to-one correspondence with the large D limit of Einstein's gravity which allows for an alternative interesting interpretation of our findings.