Non linear realizations of isometry groups, conformal algebras and geodesics in Anti-de Sitter like spaces

TL;DR

This paper explicitly constructs the global isometry and conformal groups of Anti-de Sitter-like spaces, explores their algebraic structures, and systematically computes geodesics using coset representations, enhancing understanding of their geometric and algebraic properties.

Contribution

It provides a detailed realization of isometry and conformal groups for Anti-de Sitter spaces and systematically derives geodesics via coset methods, offering new insights into their structure.

Findings

Explicit global realization of isometry groups

Realization of conformal groups at boundaries

Systematic computation of geodesics

Abstract

We present the explicit global realization of the isometries of anti-de Sitter like spaces of signature $(d_-,d_+)$, and their algebras in the space of functions on the pseudo-Riemannian symmetric space $SO(d_- +1,d_+) / SO(d_-,d_+)$. The process of going to the invariant boundaries leads to the realization of the corresponding conformal groups and algebras. We compute systematically the geodesics in these spaces by considering the coset representation of them.