One-dimensional Carrollian fluids I: Carroll-Galilei duality

TL;DR

This paper explores the duality between one-dimensional Galilean and Carrollian fluids, analyzing their dynamics as limits of Lorentzian hydrodynamics and revealing unique features of Carrollian physics.

Contribution

It introduces a duality correspondence between Galilean and Carrollian fluids and examines their dynamics and symmetries derived from Lorentzian hydrodynamics limits.

Findings

Duality exchanges longitudinal and transverse directions.

Out-of-equilibrium observables are permuted under duality.

Additional geometric structures are required for complete hydrodynamic descriptions.

Abstract

Galilean and Carrollian algebras acting on two-dimensional Newton-Cartan and Carrollian manifolds are isomorphic. A consequence of this property is a duality correspondence between one-dimensional Galilean and Carrollian fluids. We describe the dynamics of these systems as they emerge from the relevant limits of Lorentzian hydrodynamics, and explore the advertised duality relationship. This interchanges longitudinal and transverse directions with respect to the flow velocity, and permutes equilibrium and out-of-equilibrium observables, unveiling specific features of Carrollian physics. We investigate the action of local hydrodynamic-frame transformations in the Galilean and Carrollian configurations, i.e. dual Galilean and Carrollian local boosts, and comment on their potential breaking. Emphasis is laid on the additional geometric elements that are necessary to attain complete systems of hydrodynamic equations in Newton-Cartan and Carroll spacetimes. Our analysis is conducted in general Cartan frames as well as in more explicit coordinates, specifically suited to Galilean or Carrollian use.