Hydrodynamic effective field theory and the analyticity of hydrostatic correlators

Abstract

We study one-loop corrections to retarded and symmetric hydrostatic correlation functions within the Schwinger-Keldysh effective field theory framework for relativistic hydrodynamics, focusing on charge diffusion. We first consider the simplified setup with only diffusive charge density fluctuations, and then augment it with momentum fluctuations in a model where the sound modes can be ignored. We show that the loop corrections, which generically induce non-analyticities and long-range effects at finite frequency, non-trivially preserve analyticity of retarded correlation functions in spatial momentum due to the KMS constraint, as a manifestation of thermal screening. For the purposes of this analysis, we develop an interacting field theory for diffusive hydrodynamics, seen as a limit of relativistic hydrodynamics in the absence of temperature and longitudinal velocity fluctuations.

Schwinger-Keldysh effective action for relativistic Brownian particle in AdS-CFT

“…In fact, many problems, although initially formulated as (generalized) Langevin equations with certain stochastic forces, are indeed studied by converting into an action framework, see [2]. It is thus interesting to explore physical consequences of these terms by computing loop corrections to various observables, along the line of [23,25,60,61], which goes beyond the scope of present work.…”

“…It is thus natural to turn to effective field theory (EFT) approach, and construct the effective action based on symmetry principle. In recent years, in order to tackle with dissipation, the SK formalism has been applied to formulate an EFT for dissipative hydrodynamics [12][13][14][15][16][17][18][19][20][21][22][23][24][25] (see [26] for a pedagogical review). This significant achievement for hydrodynamic EFT has been largely inspired by the AdS-CFT correspondence [27][28][29], which provides a tractable framework for studying dynamics of strongly coupled large N c (the number of colors) gauge theory via weakly coupled gravitational theory in asymptotic AdS space.…”

All order effective action for charge diffusion from Schwinger-Keldysh holography

“…There is also a phenomenological interest in fluctuating hydrodynamics, largely driven by studies of quark gluon plasma (QGP), for which relativistic hydrodynamics is instrumental. Phenomenological implications of fluctuating hydrodynamics for realistic systems such as QGP have been discussed in, e.g., [37][38][39][40][41][42][43][44]. Particularly, in a model independent way, thermal fluctuations can be integrated out, resulting in emergence of "effective" TCs and shifts in positions of the hydrodynamic poles.…”

Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media

“…For a normal fluid, q * ∼ √ ω, giving rise to the renowned long-time tail phenomena [12][13][14], and consequently vanishes in the limit ω → 0 (see also refs. [46][47][48] for related discussion). Therefore, to obtain finite corrections to transport coefficients in this limit, there must be additional soft scales.…”