Carroll/fracton particles and their correspondence

Abstract

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 $GL(2,\mathbb{R})$ symmetry. We also comment on the limit from Poincaré 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).

50 pages, 2 figures; v2: References added, terminology adapted, matches published version

References in corpus (10)

• Local stabilizer codes in three dimensions without string logical operators
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Conformal Carroll groups
• Dynamics of Carroll Particles
• Field Theories with Conformal Carrollian Symmetry
• Carrollian Approach to $1+3$D Flat Holography
• Geometric action for extended Bondi-Metzner-Sachs group in four dimensions
• Carrollian conformal scalar as flat-space singleton
• Asymptotic symmetries and soft charges of fractons

Cited by in corpus (27)

• Carroll black holes
• Carrollian fluids and spontaneous breaking of boost symmetry
• Quantizing Carrollian field theories
• Super-Carrollian and Super-Galilean Field Theories
• Quantization of Carrollian conformal scalar theories
• Memory Effect and Carroll Symmetry: 50 years later
• Covariant Interacting Fractons
• Quasi-topological fractons: a 3D dipolar gauge theory
• Quantization of Carrollian fermions
• Fractonic self-duality and covariant magnetic fractons
• MultiCarroll dynamics
• Supersymmetric Carroll Galileons in Three Dimensions
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Looking for Carroll particles in two time spacetime
• Anisotropic conformal Carroll field theories and their gravity duals
• Strings as Hyper-Fractons
• Universal sectors of two-dimensional Carrollian CFTs
• Planons and their Carroll-Galilei symmetries
• Post-Carrollian Mechanics, Ideal Gas, and Gravity
• Galilei particles revisited
• Galilean and Carrollian Hodge star operators
• Emergent Carroll symmetry at phase separation in one-dimensional lattice systems
• Carrollian Lie Algebroids: Taming Singular Carrollian Geometries
• Scaling Symmetry and Carrollian Gravity
• Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs
• Rotating Carroll Black Holes: A No Go Theorem
• Strings near BTZ black holes: A Carrollian Chronicle