More about the Instanton/Soliton/Kink correspondence

TL;DR

This paper establishes a correspondence between gauge instantons in 3+1 dimensions and soliton solutions and kinks in 4+1 dimensions, revealing a unified perspective on topological solutions across dimensions.

Contribution

It demonstrates that all gauge instantons with arbitrary topological charge in 3+1 dimensions correspond to solitons and kinks in 4+1 dimensions, extending the understanding of topological solutions.

Findings

All gauge instantons with topological charge K correspond to solitons in 4+1D.

Instantons in 3+1D are linked to kink scalar fields in 4+1D.

The correspondence applies to generic topological charges.

Abstract

We demonstrate that all gauge instantons in a $d=3+1$ Yang-Mills theory, with generic topological vacuum charge K, correspond to soliton solutions and kink scalar fields in $d=4+1$ space-time.