Dynamical sectors for a spinning particle in AdS_3

TL;DR

This paper analyzes the motion of a spinning particle in AdS_3, revealing different dynamical sectors depending on mass, spin, and radius, with implications for holography and entanglement entropy in 2D CFTs.

Contribution

It identifies and characterizes the distinct dynamical sectors of a spinning particle in AdS_3, including gauge reductions and geodesic correspondences, based on mass and spin parameters.

Findings

Geodesic motion in AdS_3 for subcritical and supercritical cases.

Reduction to AdS_2 geodesics at the critical case.

Implications for holographic entanglement entropy in 2D CFTs.

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.