Dynamical sectors for a spinning particle in AdS₃

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.