Carroll/fracton particles and their correspondence

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, Double-struck capital R) symmetry.We also comment on the limit from Poincare 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).

Automated summary

We define and classify classical Carroll and fracton particles by exploiting the close relationship between the Carroll and fracton/dipole algebras, in addition to using the method of coadjoint orbits. This approach establishes a correspondence between Carroll and fracton particles, revealing the connection between Carroll energy and center-of-mass and fracton charge and dipole moment. Furthermore, we identify new massless Carrollian/neutral fractonic particles and establish a GL(2, Double-struck capital R) symmetry to relate them.