Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics

TL;DR

This paper develops stable, causal effective field theories for relativistic hydrodynamics and diffusion, incorporating statistical fluctuations and ensuring consistency with fluctuation-dissipation relations through the dynamical KMS symmetry.

Contribution

It introduces fully non-linear EFTs inspired by existing models, derived via Schwinger-Keldysh and Martin-Siggia-Rose formalisms, to describe fluctuations in relativistic fluids.

Findings

EFTs reproduce fluctuation-dissipation theorems

Multiple realizations of KMS symmetry are possible

Obstructions are identified in certain hydrodynamic models

Abstract

We construct stable and causal effective field theories (EFTs) for describing statistical fluctuations in relativistic diffusion and relativistic hydrodynamics. These EFTs are fully non-linear, including couplings to background sources, and enable us to compute n-point time-ordered correlation functions including the effects of statistical fluctuations. The EFTs we construct are inspired by the Maxwell-Cattaneo model of relativistic diffusion and M\"uller-Israel-Stewart model of relativistic hydrodynamics respectively, and have been derived using both the Martin-Siggia-Rose and Schwinger-Keldysh formalisms. The EFTs non-linearly realise the dynamical Kubo-Martin-Schwinger (KMS) symmetry, which ensures that n-point correlation functions and interactions in the theory satisfy the appropriate fluctuation-dissipation theorems. Since these EFTs typically admit ultraviolet sectors that are not fixed by the low-energy infrared symmetries, we find that they simultaneously admit multiple realisations of the dynamical KMS symmetry. We also comment on certain obstructions to including statistical fluctuations in the recently-proposed stable and causal Bemfica-Disconzi-Noronha-Kovtun model of relativistic hydrodynamics.