Hall effects in Carroll dynamics

TL;DR

This paper explores the motion of Carroll particles, revealing that massive ones are immobile due to symmetry constraints, while massless particles can move according to a generalized Hall law, with implications for exotic particles near black holes.

Contribution

It introduces a framework for Carroll particles and field theory, including the effects of central extensions and anyonic properties, and describes their dynamics under electromagnetic fields.

Findings

Massive Carroll particles are immobile due to dipole conservation.

Massless Carroll particles can follow a generalized Hall law.

Exotic photons exhibit an anyonic spin-Hall Effect near black holes.

Abstract

``Do Carroll particles move?'' The answer depends on the characteristics of the particle such as its mass, spin, electric charge, and magnetic moment. A massive Carroll particle (closely related to fractons) does not move; its immobility follows from Carroll boost symmetry which implies dipole conservation, but not conversely. A massless Carroll particle may propagate by following the Hall law, consistently with the partial breaking of the Carroll boost symmetry. The framework is extended to Carroll field theory. In $d=2$ space dimensions, the Carroll group has a two-fold central extension which allows us to generalize the dynamics to massive and massless particles, including anyons. The anyonic spin and magnetic moment combine with the doubly-extended structure parameterized by two Casimir invariants interpreted as intrinsic magnetization and non-commutativity parameter. The extended Carroll particle subjected to an electromagnetic background field moves following a generalized Hall law which includes a Zeeman force. This theory is illustrated by massless, uncharged anyons with doubly-centrally extended structure we call exotic photons, which move on the horizon of a Black Hole, giving rise to an anyonic spin-Hall Effect.