Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity

TL;DR

This paper develops a covariant Lifshitz framework to study energy-momentum dynamics and hydrodynamics at nonzero temperature, establishing a frame-independent equation of state and an ideal Lifshitz fluid both in field theory and holographic settings. It introduces a generating-functional approach and a fluid-gravity correspondence to derive the ideal hydrodynamics and the Lifshitz Ward identities, confirming the Lifshitz equation of state $\varepsilon=p$ (for zero chemical potential) and extending to charged fluids. At first order in derivatives, it identifies two additional transport coefficients (one dissipative and one dissipationless) arising in the antisymmetric part of the energy-momentum tensor and current, with Kubo formulas provided to extract them from correlators. The results offer a systematic description of dissipative processes in Lifshitz hydrodynamics, with potential applications to quantum critical systems and holographic models of strange metals, and lay groundwork for exploring anomalies and superfluid extensions.

Abstract

We consider a covariant formulation of field theories with Lifshitz scaling, and analyze the energy-momentum tensor and the scale symmetry Ward identity. We derive the equation of state and the ideal Lifshitz hydrodynamics in agreement with arXiv:1304.7481, where they were determined by using thermodynamics and symmetry properties. We construct the charged ideal Lifshitz hydrodynamics in the generating functional framework as well as in the gravitational holographic dual description. At the first viscous order, an analysis of the entropy current reveals two additional transport coefficients (one dissipative and one dissipationless) compared to the neutral case, contributing to the charge current and to the asymmetric part of the energy-momentum tensor.