Analytic non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory and transitions between them

TL;DR

This paper presents two analytic non-Abelian gravitating solitons in Einstein-Yang-Mills-Higgs theory with Nariai-type geometries, comparing their entropies and quantum properties, revealing phase differences influenced by the Higgs field.

Contribution

It introduces two new analytic solutions of gravitating solitons with distinct Higgs configurations and analyzes their entropy and quantum degeneracies.

Findings

Type I and II solitons differ in entropy and quantum degeneracy.

Higgs field VEV influences phase preference between solutions.

Type II solutions are favored when Higgs VEV exceeds a critical value.

Abstract

Two analytic examples of globally regular non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory in (3+1)-dimensions are presented. In both cases, the space-time geometries are of the Nariai type and the Yang-Mills field is completely regular and of meron type (namely, proportional to a pure gauge). However, while in the first family (type I) $X_{0} = 1/2$ (as in all the known examples of merons available so far) and the Higgs field is trivial, in the second family (type II) $X_{0}$ is not 1/2 and the Higgs field is non-trivial. We compare the entropies of type I and type II families determining when type II solitons are favored over type I solitons: the VEV of the Higgs field plays a crucial role in determining the phases of the system. The Klein-Gordon equation for test scalar fields coupled to the non-Abelian fields of the gravitating solitons can be written as the sum of a two-dimensional D'Alembert operator plus a Hamiltonian which has been proposed in the literature to describe the four-dimensional Quantum Hall Effect (QHE): the difference between type I and type II solutions manifest itself in a difference between the degeneracies of the corresponding energy levels.