Generalized BPS magnetic monopoles

We show the existence of Bogomol’nyi-Prasad-Sommerfield (BPS) magnetic monopoles in a generalized Yang-Mills-Higgs model which is controlled by two positive functions, $g({\varphi }^a{\varphi }^a)$ and $f({\varphi }^a{\varphi }^a)$. This effective model, in principle, would describe the dynamics of the nonabelian fields in a chromoelectric media. We check the consistency of our generalized construction by analyzing an explicit case ruled by a parameter $\beta$. We also use the well-known spherically symmetric Ansatz to attain the corresponding self-dual equations describing the topological solutions. The overall conclusion is that the new solutions behave around the canonical one, with smaller or greater characteristic length depending on the values of $\beta$.

Figure 1

Solutions to $H(r)$ for $\beta =-2$ (dot-dashed green line), $\beta =-1$ (dashed blue line), $\beta =0$ (usual case, solid black line), $\beta =1$ (long-dashed orange line) and $\beta =2$ (dotted red line).

Figure 2

Solutions to $W(r)$. Convention as in Fig. 1.

Figure 3

Solutions to ${\epsilon }_{\mathrm{bps}}$. Convention as in Fig. 1.

Figure 4

Solutions to $r^2{\epsilon }_{\mathrm{bps}}$. Convention as in Fig. 1.