Abstract
We find a topologically non-trivial structure of the Nambu monopole in two Higgs doublet model (2HDM), which is a magnetic monopole attached by two topologically stable $Z$ strings ($Z$ flux tubes) from two opposite sides. The structure is in sharp contrast to the topological triviality of the Nambu monopole in the standard model (SM), which is attached by a single non-topological $Z$ string. It is found that the Nambu monopole in 2HDM possesses the same fiber bundle structure with those of the `t Hooft-Polyakov monopole and the Wu-Yang description of the Dirac monopole, as a result of the fact that the electromagnetic gauge field is well-defined even inside the strings and is non-trivially fibered around the monopole, while the Nambu monopole in the SM is topologically trivial because electroweak gauge symmetry is restored at the core of the string. Consequently, the Nambu monopole in 2HDM can be regarded as an embedding of the 't Hooft-Polyakov monopole into the $SU(2)_W$ gauge symmetry, and the Dirac's quantization condition always holds, which is absent for the Nambu monopole in the SM. Furthermore, we construct a dyon configuration attached with the two strings.
Highlights
Magnetic monopoles have attracted great interest from many physicists since the seminal work by Dirac [1], which improved the asymmetry between electric and magnetic charges in the Maxwell equations and provided an explanation for the electric charge quantization
It is found that the Nambu monopole in the 2HDM possesses the same fiber-bundle structure as those of the ’t Hooft–Polyakov monopole and the Wu-Yang description of the Dirac monopole, as a result of the fact that the electromagnetic gauge field is well defined even inside the strings and is nontrivially fibered around the monopole, while the Nambu monopole in the Standard Model (SM) is topologically trivial because electroweak gauge symmetry is restored at the core of the string
We find that the electromagnetic field is well defined and regular everywhere on the sphere S2 and is nontrivially fibered like the Wu-Yang description of the Dirac monopole, despite the trivial π2.1 This is a remarkable difference from the Nambu monopole in the SM, in which the electromagnetic gauge field cannot be defined at the center of the nontopological Z string attached to the monopole since the electroweak gauge symmetry is restored there
Summary
Magnetic monopoles have attracted great interest from many physicists since the seminal work by Dirac [1], which improved the asymmetry between electric and magnetic charges in the Maxwell equations and provided an explanation for the electric charge quantization. In our previous papers [58,59] we studied the Nambu monopole in the 2HDM, which is a magnetic monopole attached with two topological Z strings from two opposite sides. We find that the electromagnetic field is well defined and regular everywhere on the sphere S2 and is nontrivially fibered like the Wu-Yang description of the Dirac monopole, despite the trivial π2.1 This is a remarkable difference from the Nambu monopole in the SM, in which the electromagnetic gauge field cannot be defined at the center of the nontopological Z string attached to the monopole since the electroweak gauge symmetry is restored there. In Appendix C we present a description in the singular gauge for the Nambu monopole in the 2HDM
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