are defined as the endpoints of the $Z$-string [@Nambu]. The $Z$-string is the classical field configuration that represents the object, which is characterized by the magnetic flux extracted from the $Z$-boson field. Namely, for a small contour $\cal C$ winding around the $Z$ - string one should have $$\int_{\cal C} Z^{\mu} dx^{\mu} \sim 2\pi;\,
 \int_{\cal C} A_{\rm EM}^{\mu} dx^{\mu} \sim 0;\,
 \int_{\cal C} B^{\mu} dx^{\mu} \sim 2\pi {\rm sin}^2\, \theta_W .$$ The string terminates at the position of the Nambu monopole. The hypercharge flux is supposed to be conserved at that point. Therefore, a Nambu monopole carries electromagnetic flux $4\pi {\rm sin}^2\, \theta_W$. The size of Nambu monopoles was estimated [@Nambu] to be of the order of the inverse Higgs mass, while its mass should be of the order of a few TeV. According to [@Nambu] Nambu monopoles may appear only in the form of a bound state of a monopole-antimonopole pair.

In lattice theory the following variables are considered as creating the $Z$ boson: $$Z_{xy} = Z^{\mu}_{x} \;
 = - {\rm sin} \,[{\rm Arg} (\Phi_x^+U_{xy} e^{i\theta_{xy}}\Phi_y) ]. \label{Z1}$$ and: $$Z^{\prime}_{xy} = Z^{\mu}_{x} \;
 = - \,[{\rm Arg} (\Phi_x^+U_{xy} e^{i\theta_{xy}}\Phi_y) ]. \label{Z1_}$$

The classical solution corresponding to a $Z$-string should 