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

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 = 1/2 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 manifests itself in a difference between the degeneracies of the corresponding energy levels.

Automated summary

The paper presents two analytic examples of globally regular non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory, comparing the characteristics of type I and type II solitons and discussing the influence of their entropies and the vacuum expectation value of the Higgs field on the phases of the system. Furthermore, it is found that the difference in degeneracies between the solutions of type I and type II in the Klein-Gordon equation for non-Abelian gravitating solitons can be used to describe the four-dimensional Quantum Hall Effect.