Carroll/fracton particles and their correspondence

TL;DR

This paper establishes a detailed correspondence between Carroll and fracton particles using algebraic methods, classifying their properties and revealing new massless particles, thus deepening understanding of fracton physics.

Contribution

It introduces a novel classification scheme linking Carroll and fracton particles via coadjoint orbits, uncovering new massless particles and symmetries.

Findings

Carroll energy and center-of-mass map to fracton charge and dipole moment.

Immobile Carroll particles correspond to fracton monopoles.

New massless Carroll and neutral fractonic particles are identified.

Abstract

We exploit the close relationship between the Carroll and fracton/dipole algebras, together with the method of coadjoint orbits, to define and classify classical Carroll and fracton particles. This approach establishes a Carroll/fracton correspondence and provides an answer to the question "What is a fracton?". Under this correspondence, carrollian energy and center-of-mass correspond to the fracton electric charge and dipole moment, respectively. Then immobile massive Carroll particles correspond to the fracton monopoles, whereas certain mobile Carroll particles ("centrons") correspond to fracton elementary dipoles. We uncover various new massless carrollian/neutral fractonic particles, provide an action in each case and relate them via a $GL(2,\mathbb{R})$ symmetry. We also comment on the limit from Poincar\'e particles, the relation to (electric and magnetic) Carroll field theories, contrast Carroll boosts with dipole transformations and highlight a generalisation to curved space ((A)dS Carroll).