On spherically symmetric ’t Hooft–Polyakov monopoles

Abstract

We consider a general spherically symmetric ansatz for [Formula: see text] connection depending on three arbitrary functions in [Formula: see text] gauge model with the triplet of scalar fields in the adjoint representation. A general analytic solution of the Bogomol’nyi equations is derived. It depends on two constants and one arbitrary function on radius. In the particular gauge, the solution coincides with Protogenov’s solutions and contains the Bogomol’nyi–Prasad–Sommerfield solution. Static spherically symmetric Euler–Lagrange equations are considered and reduced to a system of two nonlinear partial differential equations for two unknown functions.