Platonic Sphalerons in the Presence of a Dilaton Field

TL;DR

This paper constructs and analyzes symmetric sphaleron solutions in Yang-Mills-Higgs theory coupled to a dilaton, revealing their symmetries, Chern-Simons numbers, and bifurcation behavior at different dilaton couplings.

Contribution

It introduces new platonic sphaleron solutions with discrete symmetries and studies their bifurcation structure in the presence of a dilaton field.

Findings

Sphalerons with spherical, axial, tetrahedral, and cubic symmetry are constructed.

Two solution branches bifurcate at a maximal dilaton coupling constant.

Sphalerons are related to rational maps with degree N, with Chern-Simons number Q=N/2.

Abstract

We construct sphaleron solutions with discrete symmetries in Yang-Mills-Higgs theory coupled to a dilaton. Related to rational maps of degree N, these platonic sphalerons can be assigned a Chern-Simons number Q=N/2. We present sphaleron solutions with degree N=1-4, possessing spherical, axial, tetrahedral and cubic symmetry. For all these sphalerons two branches of solutions exist, which bifurcate at a maximal value of the dilaton coupling constant.