  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.
