Carroll/fracton particles and their correspondence

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