Dynamical sectors for a spinning particle in AdS_3

Abstract

We consider the dynamics of the motion of a particle of mass M and spin J in AdS_3. The study reveals the presence of different dynamical sectors depending on the relative values of M, J and the AdS_3 radius R. For the subcritical M^2 R^2-J^2 >0 and supercritical M^2 R^2-J^2<0 cases, it is seen that the equations of motion give the geodesics of AdS_3. For the critical case M^2R^2=J^2 there exist extra gauge transformations which further reduce the physical degrees of freedom, and the motion corresponds to the geodesics of AdS_2. This result should be useful in the holographic interpretation of the entanglement entropy for 2d conformal field theories with gravitational anomalies.

arXiv comment12 pages, 1 figure, Some comments, references and formulas are added

References in corpus (10)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Geometry of the 2+1 Black Hole
• The exotic Galilei group and the "Peierls substitution"
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Anyon wave equations and the noncommutative plane
• Holographic entanglement entropy and gravitational anomalies
• (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
• Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• On the negative spectrum of the 2+1 black hole

Cited by in corpus (4)

• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• Colourful Poincaré symmetry, gravity and particle actions
• Quantization of the ${\mathrm{AdS}}_3$ Superparticle on $\mathrm{OSP}(1|2{)}^2/\mathrm{SL}(2,\mathbb{R})$
• A general action for a particle in 2+1 anti-de Sitter space