Analytic long-lived modes in charged critical plasma

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.