A Note on the Julia-Zee Dyon Solution

Abstract

We observed that the Julia-Zee dyon solution can be presented in similar exact form when the $\phi$-winding number of the internal space is $n$. However the closed form $n$-monopole version of the Julia-Zee dyon solution exits in the present of $(n-1)$ string antimonopoles. Hence the net monopole charge of the system at large distances is still unity. When $n=1$, the solution is just the Julia-Zee dyon solution. Using the ansatz of this solution, we also present the antimonopole version of the Julia-Zee dyon in closed form, with all the magnetic field directions reversed. We would also like to note that for a given monopole charge in this dyon solution, the net electric charge of the system can be both positive and negative.