Effective field theory of dissipative fluids

TL;DR

This paper develops an effective field theory framework for dissipative fluids that captures nonlinear noise interactions, symmetries, and emergent supersymmetry, providing a systematic approach to fluctuating hydrodynamics.

Contribution

It introduces a path integral formulation of fluctuating hydrodynamics with nonlinear noise interactions and identifies key symmetries, including a novel supersymmetry in the classical limit.

Findings

Derivation of a path integral formulation for fluctuating hydrodynamics

Identification of symmetries including a local KMS condition and supersymmetry

Extension of Onsager relations to nonlinear regimes

Abstract

We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional $Z_2$ symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.