Dynamical sectors for a spinning particle in AdS₃

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We consider the dynamics of the motion of a particle of mass M and spin J in AdS₃. The study reveals the presence of different dynamical sectors depending on the relative values of M, J and the AdS₃ radius R. For the subcritical M² R²-J² >0 and supercritical M² R²-J²<0 cases, it is seen that the equations of motion give the geodesics of AdS₃. For the critical case M²R²=J² there exist extra gauge transformations which further reduce the physical degrees of freedom, and the motion corresponds to the geodesics of AdS₂. This result should be useful in the holographic interpretation of the entanglement entropy for 2d conformal field theories with gravitational anomalies.