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arXiv · 2608.02732

Particle-Vortex Duality of Hydrodynamics

Cenke Xu·Matthew P. A. Fisher
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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 $U(1)^{(1)}_e$, as well as $U(1)_v$ associated with the conservation of vortices. This duality provides a bridge between the hydrodynamics of matter and magnetohydrodynamics.

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Cenke Xu, Matthew P. A. Fisher. 2026-08-03. Particle-Vortex Duality of Hydrodynamics. https://arxiv.org/abs/2608.02732

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