Effective Chern-Simons actions of particles coupled to 3D gravity

Abstract

Point particles in 3D gravity are known to behave as topological defects, while gravitational field can be expressed as the Chern-Simons theory of the appropriate local isometry group of spacetime. In the case of the Poincaré group, integrating out the gravitational degrees of freedom it is possible to obtain the effective action for particle dynamics. We review the known results, both for single and multiple particles, and attempt to extend this approach to the (anti-)de Sitter group, using the factorizations of isometry groups into the double product of the Lorentz group and AN(2) group. On the other hand, for the de Sitter group one can also perform a contraction to the semidirect product of AN(2) and the translation group. The corresponding effective action curiously describes a Carrollian particle with the AN(2) momentum space. We derive this contraction in a more rigorous manner and further explore its properties, including a generalization to the multiparticle case.

arXiv comment15 pages, v2 several formulae, remarks and references added, v3 summary extended and references added

References in corpus (30)

• Non-Abelian Anyons and Topological Quantum Computation
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
• Dynamics of Carroll Particles
• Doubly Special Relativity and de Sitter space
• Symplectic structure of the moduli space of flat connections on a Riemann surface
• Relative locality: A deepening of the relativity principle
• Carroll symmetry of plane gravitational waves
• Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry
• Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity
• Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity
• Topological field theory and the quantum double of SU(2)
• Quaternionic and Poisson-Lie structures in 3d gravity: the cosmological constant as deformation parameter
• Conformal symmetry of the coupled Chern-Simons and gauged nonlinear Schrödinger equations
• Symmetries of quantum space-time in 3 dimensions
• The Phase Space Structure of Multi Particle Models in 2+1 Gravity
• Geometrical (2+1)-gravity and the Chern-Simons formulation: Grafting, Dehn twists, Wilson loop observables and the cosmological constant
• Phase space structure of Chern-Simons theory with a non-standard puncture
• Effective particle kinematics from Quantum Gravity
• Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups
• Doubly Special Relativity as a Limit of Gravity
• Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity
• Deformed Carroll particle from 2+1 gravity
• Anyonic statistics and large horizon diffeomorphisms for Loop Quantum Gravity Black Holes
• Beyond Fock space in three dimensional semiclassical gravity
• Gauge Theories and Fibre Bundles - Applications to Particle Dynamics
• $\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant
• Multi-particle systems in $\kappa$-Poincaré inspired by 2+1D gravity

Cited by in corpus (6)

• Planar Carrollean dynamics, and the Carroll quantum equation
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• Quantum $D=3$ Euclidean and Poincaré symmetries from contraction limits
• 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
• On Carrollian and Galilean contractions of BMS algebra in 3 and 4 dimensions