Sphaleron of a 4 dimensional SO(4) Higgs model

TL;DR

This paper constructs a finite energy transition path between topologically distinct vacua in a 4D SO(4) Higgs model, identifying a sphaleron at the energy barrier's peak with a specific Chern-Simons number.

Contribution

It introduces a geometric loop construction to explicitly identify the sphaleron solution in a 4D SO(4) Higgs model, linking topological vacua and energy barriers.

Findings

Identifies a sphaleron at the energy barrier with N_CS=1/2.

Constructs a finite energy path between vacua using Manton's geometric loop method.

Demonstrates the existence of a topologically nontrivial sphaleron in the model.

Abstract

We construct the finite energy path between topologically distinct vacua of a 4 dimensional SO(4) Higgs model which is known to support an instanton, and show that there is a sphaleron with Chern-Simons number N_CS=1/2 at the top of the energy barrier. This is carried out using the original geometric loop construction of Manton.