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.

arXiv comment24+1 pages. v2: References added, typos fixed, matches version published in JHEP

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• Corrections to diffusion in interacting quantum systems
• Second order equilibrium transport in strongly coupled $\mathcal{N}=4$ supersymmetric $SU(N_c)$ Yang-Mills plasma via holography
• Holographic Schwinger-Keldysh field theory of SU(2) diffusion
• A Bound on Thermalization from Diffusive Fluctuations
• Nearly Critical Superfluids in Keldysh-Schwinger Formalism
• Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media
• Holographic Schwinger-Keldysh effective field theories including a non-hydrodynamic mode
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Analytic structure of diffusive correlation functions
• Universality of pseudo-Goldstone damping near critical points
• Higher-group global symmetry and the bosonic M5 brane
• Dirac fermions under imaginary rotation