Non-equilibrium charge-vortex duality

TL;DR

This work extends charge–vortex dualities to non-equilibrium, finite-temperature fluids by mapping two-fluid hydrodynamics to a tensor gauge theory through a finite-temperature effective action. It builds a dual description with gauge fields, where vortices become charges, and identifies two vortex species with distinct mobility constraints, including fracton-like behavior for normal-component vortices. The analysis yields Liénard–Wiechert–type wave dynamics with coupling-induced velocity corrections $v_N$ and $v_S$ and computes gauge-field correlators that exhibit dynamical cross-coupling between the normal and superfluid sectors. Overall, the framework provides a non-equilibrium, gauge-theoretic route to study strongly coupled fluids via a weakly coupled dual and opens avenues for exploring fracton-like defect dynamics in fluid systems.

Abstract

Traditionally applied within equilibrium states, the charge-vortex dualities are expanded to address the complex dynamics of superfluids and ideal fluids under non-static conditions. We have constructed explicit mappings of finite temperature fluid dynamics to gauge theories, enabling a dual description where vortices in both superfluids and ideal fluids are interpreted as charges within these theories. We found that vortices in the normal component naturally exhibit mobility restrictions, as manifested by the symmetries and conservation laws. Next, we formulated the Liénard-Wiechert problem for the ideal fluid at finite temperature and extracted the wave dynamics in the system along with the speed of sound corrections for both fluid components. Finally, we computed the correlation functions for the gauge potentials, particularly elucidating explicit cross-correlations between the normal and superfluid components.