Effective field theory of dissipative fluids

TL;DR

The paper presents an effective field theory for dissipative fluids by embedding hydrodynamic long-wavelength modes into a closed-time-path path integral with doubled degrees of freedom. It introduces a fluid spacetime of Stueckelberg fields X^μ_s and a timelike τ, imposes emergent spacetime symmetries, and enforces a local KMS condition that yields standard hydrodynamic constraints and nonlinear Onsager relations, while revealing an emergent supersymmetry in the classical statistical limit. Through concrete constructions for diffusion and charged fluids, it unifies fluctuating hydrodynamics with BRST symmetry and provides a systematic framework to derive constitutive relations, non-equilibrium FDT, and correlation functions to arbitrary order in derivatives and noises. The approach recovers the familiar stochastic hydrodynamics at leading order and predicts nontrivial nonlinear relations and positivity constraints at higher orders, offering a principled route to study fluctuations in non-equilibrium fluids with potential applications to holography, critical dynamics, and transport phenomena.

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.

Figures (2)

• Figure 1: Relations between the fluid spacetime and two copies of physical spacetimes. The red straight line in the fluid spacetime with constant $\sigma^i$ is mapped by $X^\mu_{1,2} (\sigma^0, \sigma^i)$ to physical spacetime trajectories (also in red) of the corresponding fluid element. In the holographic context, the fluid spacetime corresponds to the horizon hypersurface, and the two copies of physical spacetimes correspond to two asymptotic boundaries of AdS. $X^\mu_{1,2}$ describe relative embeddings of these hypersurfaces.
• Figure 2: (a) Evolution of a general initial density matrix $\rho_0$. (b) Closed time path contour from taking the trace. Inserted operators should be path ordered as indicated by the arrows.