Particle-Vortex Duality of Hydrodynamics

Abstract

Equipped with the recently recognized symmetry structure of mixed states of matter and "strong-weak spontaneous symmetry breaking" (SW-SSB), we develop a quantum particle-vortex duality of emergent model-F and model-A hydrodynamics of 2d boson/rotor systems. This duality relation demonstrates that classical hydrodynamics of 2d bosons can be described in terms of the charge symmetry $U(1{)}_c$, but also equivalently in terms of the dual (emergent) 1-form symmetry $U(1{)}_e^{(1)}$, as well as $U(1{)}_v$ associated with the conservation of vortices. This duality provides a bridge between the hydrodynamics of matter and magnetohydrodynamics.

17 pages 1 figure