Excited Platonic Sphalerons in the Presence of a Dilaton Field

TL;DR

This paper constructs and analyzes excited platonic sphaleron solutions with discrete symmetries in Yang-Mills-Higgs theory coupled to a dilaton, revealing new excited states with complex energy density structures.

Contribution

It introduces excited platonic sphalerons in the presence of a dilaton, expanding the understanding of solutions related to rational maps with discrete symmetries.

Findings

Existence of excited platonic sphalerons with N=4 cubic symmetry

Two branches of first excited states identified

Energy density exhibits a cube within a cube structure

Abstract

We construct sphaleron solutions with discrete symmetries in Yang-Mills-Higgs theory coupled to a dilaton. These platonic sphalerons are related to rational maps of degree N. We demonstrate that, in the presence of a dilaton, for a given rational map excited platonic sphalerons exist beside the fundamental platonic sphalerons. We focus on platonic sphaleron solutions with N=4, which possess cubic symmetry, and construct the two branches of their first excitations. The energy density of these excited platonic sphalerons exhibits a cube within a cube.