Exact Schwarzschild-like solution for SU(N) gauge theory

In this paper we extend our previously discovered exact solution for an SU(2) Yang-Mills-Higgs theory, to the general group SU(N + 1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similiar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite on a spherical shell of radius r(0) = K. However in the Schwarzschild case the singularity at the event horizon is a coordinate singularity while for the present solution the singularity is a true singularity. It is speculated that this solution may give a confinement mechanism for non-Abelian gauge theories, since any particle which carries the SU(N + 1) charge would become permanently trapped inside the region r < r(0).