Dissipation in the effective field theory for hydrodynamics: First order effects

TL;DR

The paper develops an effective field theory for relativistic hydrodynamics that incorporates dissipation by coupling the hydrodynamic EFT fields to a thermalized microscopic sector. Using the in-in formalism and linear-order couplings to composite operators from the bath, it derives low-frequency dissipation characterized by the transport coefficients $\zeta$, $\eta$, and, for charged fluids, the heat conduction coefficient $\chi$, with the Kubo relations recovered from the EFT. For a neutral fluid, symmetry fixes the leading dissipative couplings and yields the standard $k^2$ attenuation of sound and shear modes, identifying $\zeta=A_0$ and $\eta=A_2$ in the Kubo limit. For fluids with conserved charge, a minimal two-parameter extension is proposed and matched to known hydrodynamic results, fixing the coefficients and incorporating heat conduction; the work lays groundwork for a coset-based, higher-order extension and connects hydrodynamic dissipation with broader EFT and thermalization concepts, including insights relevant to black-hole physics.

Abstract

We introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory to a generic sector that "lives in the fluid", which corresponds physically to the microscopic constituents of the fluid. At linear order in perturbations, the symmetries, the derivative expansion, and the assumption that this microscopic sector is thermalized, allow us to characterize the leading dissipative effects at low frequencies via three parameters only, which correspond to bulk viscosity, shear viscosity, and--in the presence of a conserved charge--heat conduction. Using our methods we re-derive the Kubo relations for these transport coefficients.

Figures (1)

• Figure 1: Feynman diagram representation of eq. (\ref{['Dyson series']}): the solid lines represent the $\phi$ propagators and the gray circles the two-point function of $\mathcal{O}$.