A general action for a particle in 2+1 anti-de Sitter space
Abstract
We discuss a general action for a particle in AdS 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/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 Lagrangian, we obtain an AdS Lagrangian which is the same, although expressed in different variables, that the general AdS one, and from this one can identify the extra gauge transformations appearing in the critical sectors of the AdS theory. A differential equation connecting the AdS AdS chiral variables to the AdS covariant ones is obtained, and it is explicitly solved at first order in the Goldstone bosons associated to boosts and rotations.
Keywords
Cite
@article{arxiv.2509.18959,
title = {A general action for a particle in 2+1 anti-de Sitter space},
author = {Carles Batlle and Joaquim Gomis},
journal= {arXiv preprint arXiv:2509.18959},
year = {2025}
}
Comments
This paper was published in a special issue of Geometric Mechanics dedicated to the memory of Miguel Carlos {Mu\~noz}-Lecanda