Monopoles and dyons in the SU(5) model

Abstract

The spherically symmetric monopoles and dyons of the SU(5) model of grand unification (without quarks and leptons) are discussed. It is shown that such monopoles and dyons can exist only in the sectors corresponding to magnetic charges $m=\pm \frac{1}{2e}, \pm \frac{1}{e}, \pm \frac{3}{2e}, \mathrm{and} \pm \frac{2}{e}$, where $e$ is the charge of the positron. We investigate in detail the properties of the dyons with the smallest possible magnetic charge ($\mathrm{}\left|m\right|=\frac{1}{2e}$). By semiclassical reasoning we show that apart from the magnetic charge the properties of the dyons are described by two quantum numbers $n$ and $k$. The dyons come in families, denoted by $n=0,1,2,\dots$, with electric charge $q_n=n(-\frac{4e}{3})$, baryon minus lepton number $=n(-\frac{2}{3})$, and the $k\mathrm{th}$ member of the $n\mathrm{th}$ family ($k=0,1,2,\dots$) transforms according to the ($n+k$,$k$) for $n\ge 0$ or the ($k$,$\mathrm{}\left|n\right|+k$) for $n<\mathrm{}0\mathrm{}$ representation of $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_C$. We argue that all the members of a given family are degenerate at the level we are working. This degeneracy is expected to be lifted in the full quantum theory, in which case each family collapses to one stable dyon, characterized by one integer $n$ and whose quantum numbers are as follows: It has electric charge $=n(-\frac{4e}{3})$ and baryon number minus lepton number $=n(-\frac{2}{3})$, and it transforms under $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_C$ like the symmetric combination of $n$ 3's for $n\ge 0$, or $\mathrm{}\left|n\right|\mathrm{} \overline{3}$'s for $n<\mathrm{}0\mathrm{}$. Interesting processes involving monopoles and dyons are discussed; we show, for example, that the presence of a dyon strongly enhances baryon-number-violating processes. Finally, a less detailed discussion of poles with the other possible magnetic charges is included.