Carroll in Shallow Water

TL;DR

This paper uncovers a novel link between Carrollian symmetries and shallow water hydrodynamics, showing that wave actions correspond to sectors of Carrollian electrodynamics, revealing deep symmetry structures in fluid models.

Contribution

It demonstrates a surprising connection between Carrollian symmetries and shallow water wave equations through a gauge theoretic framework, linking fluid dynamics to Carrollian electrodynamics.

Findings

Flat band and Poincaré wave actions map to Carrollian electrodynamics sectors

Reveals symmetry structures underlying shallow water equations

Establishes a new theoretical bridge between fluid dynamics and Carrollian physics

Abstract

We discover a surprising connection between Carrollian symmetries and hydrodynamics in the shallow water approximation. Carrollian symmetries arise in the speed of light going to zero limit of relativistic Poincar\'e symmetries. Using a recent gauge theoretic description of shallow water wave equations we find that the actions corresponding to two different waves, viz. the so called flat band solution and the Poincar\'e waves map exactly to the actions of the electric and magnetic sectors of Carrollian electrodynamics.