A general action for a particle in 2 + 1 anti-de Sitter space

In this paper, we discuss a general action for a particle in AdS 3 using the nonlinear realization framework. Critical sectors are found and characterized in terms of the parameters appearing in the Lagrangian, generalizing the known results for AdS 3 /SO(2). A study of the dynamics of this system and of the geometrical meaning of the new terms in the action is also undertaken. Using two chiral copies of the general AdS 2 Lagrangian, we obtain an AdS 3 Lagrangian which is the same, although expressed in different variables, that the general AdS 3 one, and from this one can identify the extra gauge transformations appearing in the critical sectors of the AdS 3 theory. A differential equation connecting the AdS 2 [Formula: see text]×[Formula: see text]AdS 2 chiral variables to the AdS 3 covariant ones is obtained, and it is explicitly solved at first order in the Goldstone bosons associated to boosts and rotations.