Towards an effective action for relativistic dissipative hydrodynamics

TL;DR

This work constructs an effective action for relativistic dissipative hydrodynamics that includes thermal fluctuations by coupling hydrodynamic fields to stochastic noise within a functional integral framework. Starting from noisy conservation laws, the authors derive a quadratic $S_{ m eff}$ for the hydrodynamic variables and auxiliary response fields, discuss discretization and the necessity of a Jacobian, and show how loop corrections from fluctuations can renormalize transport coefficients such as $ta$, $zeta$, and $sigma$. They introduce explicit noise fields and ghost sectors to maintain a consistent path integral, and argue that the resulting framework provides a systematic route to compute real-time correlation functions while capturing nontrivial fluctuation effects beyond tree-level hydrodynamics. The authors also identify technical challenges, including UV divergences, frame invariance, and coupling to external sources on the Schwinger-Keldysh contour, outlining future work to realize a fully covariant, fluctuation-inclusive description of relativistic dissipative fluids.

Abstract

We propose an effective action for first order relativistic dissipative hydrodynamics that can be used to evaluate n-point symmetrized correlation functions, taking into account thermal fluctuations of the hydrodynamic variables.

Figures (1)

• Figure 1: How $T^{\mu\nu}$ should be discretized. $T^{\mu\nu}$ is the flux of $P^\nu$ from one site to the neighboring site in the $\mu$-direction. Stress-energy conservation at a site is the equality of the sum of all incoming $P^\nu$ contributions and the sum of all outgoing $P^\nu$ contributions.