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.
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A smooth finite-energy monopole in an Yang-Mills theory with an adjoint Higgs field uses the normalized Higgs direction at infinity to define a map . 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 .