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/Aristotle 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.
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Acknowledgments
We thank Andrew Beckett, Jelle Hartong, Emil Have and Jakob Salzer for useful discussions and Simon Pekar for a careful reading of an earlier version of this draft. The research of AP is partially supported by Fondecyt grants No 1211226, 1220910 and 1230853. SP is supported by the Leverhulme Trust Research Project Grant (RPG-2019-218) “What is Non-Relativistic Quantum Gravity and is it Holographic?”.
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Figueroa-O’Farrill, J., Pérez, A. & Prohazka, S. Quantum Carroll/fracton particles. J. High Energ. Phys. 2023, 41 (2023). https://doi.org/10.1007/JHEP10(2023)041
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DOI: https://doi.org/10.1007/JHEP10(2023)041