Deformed Carroll particle from 2+1 gravity

Abstract

We consider a point particle coupled to 2+1 gravity, with de Sitter gauge group SO(3,1). We observe that there are two contraction limits of the gauge group: one resulting in the Poincare group, and the second with the gauge group having the form AN(2) \ltimes \an(2)^*. The former case was thoroughly discussed in the literature, while the latter leads to the deformed particle action with de Sitter momentum space, like in the case of kappa-Poincare particle. However, the construction forces the mass shell constraint to have the form p_0^2 = m^2, so that the effective particle action describes the deformed Carroll particle.

10 pages

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Cited by in corpus (13)

• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• The $\kappa$-Newtonian and $\kappa$-Carrollian algebras and their noncommutative spacetimes
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• Carroll membranes
• Quantum $D=3$ Euclidean and Poincaré symmetries from contraction limits
• Multi-particle systems in $\kappa$-Poincaré inspired by 2+1D gravity
• $\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant
• Effective Chern-Simons actions of particles coupled to 3D gravity
• Quantum symmetries in 2+1 dimensions: Carroll, (a)dS-Carroll, Galilei and (a)dS-Galilei
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• Spacetime defects and group momentum space
• Three-dimensional gravity and deformations of relativistic symmetries
• On Carrollian and Galilean contractions of BMS algebra in 3 and 4 dimensions