Topological structure of Nambu monopole in Two Higgs doublet models -- Fiber bundle, Dirac's quantization and dyon --

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.