Author:
Canfora Fabrizio,Oh Seung Hun
Abstract
AbstractTwo 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) $$X_{0} = 1/2$$
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) $$X_{0} = 1/2$$
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.
Funder
National Research Foundation of Korea
Fondo Nacional de Desarrollo Científico y Tecnológico
Publisher
Springer Science and Business Media LLC
Subject
Physics and Astronomy (miscellaneous),Engineering (miscellaneous)
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