Dynamical symmetries, coherent states and nonlinear realizations: the SO(2,4) case

TL;DR

This paper explores nonlinear realizations of the SO(4,2) symmetry group, introducing models, coherent states, and a spontaneous compactification mechanism, with implications for symmetry breaking and gauge theories.

Contribution

It presents new models and a compactification mechanism within the nonlinear realization framework of SO(4,2), expanding understanding of symmetry breaking.

Findings

Construction of linear and quadratic curvature models

Definition of Klauder-Perelomov coherent states for these models

Introduction of a spontaneous compactification mechanism

Abstract

Nonlinear realizations of the SO(4,2) group are discussed from the point of view of symmetries. Dynamical symmetry breaking is introduced. One linear and one quadratic model in curvature are constructed. Coherent states of the Klauder-Perelomov type are defined for both cases taking into account the coset geometry. A new spontaneous compactification mechanism is defined in the subspace invariant under the stability subgroup. The physical implications of the symmetry rupture in the context of non-linear realizations and direct gauging are analyzed and briefly discussed.