Linearized hydrodynamics from probe-sources in the gauge-string duality

TL;DR

The paper analyzes how a strongly coupled N=4 plasma responds to generic localized probe sources in the gauge–string duality framework, revealing that the large-distance energy–momentum tensor comprises a bath term, a linearized hydrodynamic piece, and a non-hydrodynamic correction 𝔽_{mn} that can compete with viscous effects. It provides a detailed procedure to extract ⟨T_{mn}⟩ from bulk sources, demonstrates the non-conservation ∂^m⟨T_{mn}⟩ = J_{n5}^{(3)}, and derives the conditions under which diffusion wakes or sonic disturbances arise, including explicit analyses for strings and point particles. The work identifies how near-boundary and near-horizon analyses combine via matched asymptotics to produce a resummed hydrodynamic description with an effective hydro four-force density F^{hydro}, and it highlights divergences tied to infinite quark masses as localized contact terms. Overall, the results refine our understanding of energy deposition and wake formation in strongly coupled plasmas, with implications for jet quenching phenomenology in gauge–gravity models.

Abstract

We study the response of an infinite, asymptotically static N=4 plasma to a generic localized source in the probe approximation. At large distances, the energy momentum tensor of the plasma includes a term which satisfies the constitutive relations of linearized hydrodynamics, but it can also include a non-hydrodynamical term which contributes at the same order as viscous corrections, or even at leading order in some cases. The conditions for the appearance of a laminar wake far behind the source and its relevance for phenomenological models used to explain di-hadron correlations are discussed. We also consider the energy momentum tensor near the source, where the hydrodynamical approximation can be expected to break down. Our analysis encompasses a wide range of sources which are localized in the bulk of AdS, including trailing strings, mesonic and baryonic configurations of strings, and point particles.