Topological Solitons from DeConstructed Extra Dimensions

TL;DR

This paper explores how topological monopole-like configurations in higher-dimensional Yang-Mills theories manifest as novel solutions in the effective 3+1 dimensional theory, revealing a connection between extra dimensions and monopole solutions.

Contribution

It demonstrates the emergence of gauged-bosonic Skyrmions and their evolution into 't Hooft--Polyakov monopoles through dimensional reduction and spontaneous symmetry breaking.

Findings

Existence of monopole-like solutions in 4+1D Yang-Mills theories.

Identification of these solutions as gauged-bosonic Skyrmions in 3+1D.

Transition to 't Hooft--Polyakov monopoles upon symmetry breaking.

Abstract

A topological monopole-like field configuration exists for Yang-Mills gauge fields in a 4+1 dimensions. When the extra dimension is compactified to 3+1 dimensions with periodic lattice boundary conditions, these objects reappear in the low energy effective theory as a novel solution, a gauged-bosonic Skyrmion. When the low energy theory spontaneously breaks, the Nambu-Goldstone mode develops a VEV, and the gauged-bosonic Skyrmion morphs into a `t Hooft--Polyakov monopole.