Generalized dyons and magnetic dipoles: The issue of angular momentum

It is known that a non-Abelian magnetic monopole cannot rotate globally (although it may possess a nonzero angular momentum density). At the same time, the total angular momentum of a magnetic dipole equals the electric charge. In this work we question the generality of these results by considering a number of generalizations of the Georgi-Glashow model. We study two different types of finite energy, regular configurations: solutions with net magnetic charge and monopole-antimonopole pairs with zero net magnetic charge. These configurations are endowed with an electric charge and carry also a nonvanishing angular momentum density. However, we argue that the qualitative results found in the Georgi-Glashow model are generic and thus a magnetic monopole cannot spin as long as the matter fields feature the usual “monopole” asymptotic behavior independently of the dynamics of the model. A study of the properties of the dyons and magnetic dipoles in some generalizations of the Georgi-Glashow model supplemented with higher order Skyrme-like terms in the gauge curvature and Higgs fields is given quantitatively.

Figure 1

The mass $M$ and the electric charge $Q_e$ are shown as a function of the coupling constant ${\lambda }_0$ for type (I) spherically symmetric generalized dyon solutions. Several values of the electric potential $V_0$ are considered. The bottom panel is a zoom-in plot of the top one. Here and in Figs. 2, 3, 4, 5, 6, $M$ and $Q_e$ are normalized with respect to the corresponding solutions in the Georgi-Glashow model with the same $V_0$.

Figure 2

The mass $M$ and the electric charge $Q_e$ are shown as a function of the coupling constant ${\lambda }_3$ for type (II) spherically symmetric generalized dyon solutions for several values of the electric potential $V_0$.

Figure 3

The mass $M$ and the electric charge $Q_e$ are shown as a function of the coupling constant ${\lambda }_0$ for type (I) axially symmetric generalized dyon solutions. Several values of the electric potential $V_0$ are considered. The solutions here and in Figure 4 have a winding number $n=2$.

Figure 4

The mass $M$ and the electric charge $Q_e$ are shown as a function of the coupling constant ${\lambda }_3$ for type (II) axially symmetric generalized dyon solutions and three values of the electric potential $V_0$.

Figure 5

Same as Fig. 3 for electrically charged, generalized dipole solutions. Here and in Fig. 6 the winding number is $n=1$.

Figure 6

Same as Fig. 4 for electrically charged, generalized dipole solutions.