Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry

Abstract

We consider Chern-Simons theories for the Poincare, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern-Simons formulation of 3d gravity. We determine conditions under which kappa-Poincare symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vector as deformation parameter, we find that such an association is possible only in the de Sitter case, and that the associated Chern-Simons action is not the gravitational one. Although the resulting theory and 3d gravity have the same equations of motion for the gauge field, they are not equivalent, even classically, since they differ in their symplectic structure and the coupling to matter. We deduce that kappa-Poincare symmetry is not associated to either classical or quantum gravity in three dimensions. Starting from the (non-gravitational) Chern-Simons action we explain how to construct a multi-particle model which is invariant under the classical analogue of kappa-de Sitter symmetry, and carry out the first steps in that construction.

arXiv comment31 pages, minor corrections and additional comments

References in corpus (16)

• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Symplectic structure of the moduli space of flat connections on a Riemann surface
• 2+1 gravity and Doubly Special Relativity
• Braided Momentum Structure of the q-Poincare Group
• Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group
• 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
• 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
• Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups
• Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity
• q-Deformation and Semidualisation in 3d Quantum Gravity
• Grafting and Poisson structure in (2+1)-gravity with vanishing cosmological constant
• Dual generators of the fundamental group and the moduli space of flat connections

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