 't Hooft–Polyakov monopole

A smooth finite-energy monopole in an $SU(2)$ Yang-Mills theory with an adjoint Higgs field uses the normalized Higgs direction at infinity to define a map $S_{\infty }^2\to S^2$. Its nonzero degree supplies the magnetic topological sector. Unlike a singular Abelian Dirac monopole, the non-Abelian gauge and Higgs fields can have a regular core. In the zero-potential limit the Bogomolny-Prasad-Sommerfield monopole equations are $B_i=\pm D_i\Phi$.

The 't Hooft–Polyakov monopole is a theoretical solution in the context of gauge theories, specifically in the study of magnetic monopoles within non-Abelian gauge theories. It was independently discovered by Gerard 't Hooft and Alexander Polyakov in the 1970s.