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

Abstract

We discuss a general action for a particle in AdS${}_3$ using the non-linear 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${}_2\times$ 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.

arXiv commentThis paper was published in a special issue of Geometric Mechanics dedicated to the memory of Miguel Carlos {Muñoz}-Lecanda

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