Spin Distribution for the ’t Hooft–Polyakov Monopole in the Geometric Theory of Defects

Mikhail O Katanaev

doi:10.3390/universe7080256

Abstract

Recently the ’t Hooft–Polyakov monopole solutions in Yang–Mills theory were given new physical interpretation in the geometric theory of defects describing the continuous distribution of dislocations and disclinations in elastic media. It means that the ’t Hooft–Polyakov monopole can be seen, probably, in solids. To this end we need to compute the corresponding spin distribution on lattice sites of crystals. The paper describes one of the possible spin distributions. The Bogomol’nyi–Prasad–Sommerfield solution is considered as an example.

Highlights

We note that the geometric theory of defects is a more general model describing the distribution of dislocations that are defects in elastic media itself
The famous ’t Hooft–Polyakov monopoles [21,22] are the exact solutions of the field equations in the SU (2) gauge theory interacting with the triplet of scalar fields in the adjoint representation and λφ4 -type interaction
In the geometric theory of defects, we consider functional (1) as the expression for the free energy describing static distribution of disclinations and dislocations in elastic media with defects, the triplet of scalar fields being the source of defects

Summary

Introduction

Hooft–Polyakov Monopole in the Geometric Theory of Defects. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. We note that the geometric theory of defects is a more general model describing the distribution of dislocations that are defects in elastic media itself. These defects correspond to nontrivial torsion, the latter having physical interpretation as the surface density of the Burgers vector of dislocations. It was noted that the ’t Hooft–Polyakov monopole has straightforward physical interpretation in the geometric theory of defects describing media with continuous distribution of disclinations and dislocations [20].

The ’t Hooft–Polyakov Monopole

Distributions of Spins

Conclusions