Hydrodynamic effective field theory and the analyticity of hydrostatic correlators

TL;DR

This paper investigates one-loop corrections to hydrostatic correlation functions in relativistic hydrodynamics, demonstrating that analyticity in spatial momentum is preserved due to thermal screening effects, within an effective field theory framework.

Contribution

It develops an interacting field theory for diffusive hydrodynamics and analyzes the impact of loop corrections on correlation function analyticity.

Findings

Loop corrections induce non-analyticities and long-range effects.

Retarded correlation functions maintain analyticity in spatial momentum.

Thermal screening preserves analyticity despite quantum corrections.

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.