Quantum Carroll/fracton particles

TL;DR

This paper classifies and relates elementary quantum particles in Carroll and fracton theories, revealing their unique properties and implications for holography and ultralocal field theories.

Contribution

It establishes a correspondence between Carroll and fracton particles and expresses their representations through free field equations on spacetime.

Findings

Massive Carroll and fracton theories are ultralocal.

Distinct differences between massless and magnetic Carroll theories.

Implications for flat space holography.

Abstract

We classify and relate unitary irreducible representations (UIRs) of the Carroll and dipole groups, i.e., we define elementary quantum Carroll and fracton particles and establish a correspondence between them. Whenever possible, we express the UIRs in terms of fields on Carroll/aristotelian spacetime subject to their free field equations. We emphasise that free massive (or "electric") Carroll and fracton quantum field theories are ultralocal field theories and highlight their peculiar and puzzling thermodynamic features. We also comment on subtle differences between massless and "magnetic" Carroll field theories and discuss the importance of Carroll and fractons symmetries for flat space holography.