The Chiral 2-Sphere

TL;DR

This paper develops a detailed theoretical framework for the chiral 2-sphere, modeling it as a low-energy effective theory with Goldstone bosons arising from broken SU(2) symmetry.

Contribution

It provides a comprehensive construction of the chiral 2-sphere framework in various coordinate systems, enhancing understanding of Goldstone bosons in this context.

Findings

Explicit parametrization of the chiral 2-sphere

General coordinate system formulations

Foundations for low-energy effective theories

Abstract

The two dimensional surface of a sphere can be parametrized by coordinates representing two charged pions acting as Goldstone bosons of a broken $SU_2$ symmetry. We construct in full concrete detail, and in a general class of coordinate systems, all the relevant structure forming a framework for this low energy effective theory.