EXACT SCHWARZSCHILD-LIKE SOLUTION FOR SU(N) GAUGE-THEORY

In this paper we extend our previously discovered exact solution for a n SU(2) Yang-Mills-Higgs theory, to the general group SU(N + 1). Using the first-order formalism of Bogomolny, an exact, spherically symmetr ic 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 r adius r(0) = K. However in the Schwarzschild case the singularity at t he event horizon is a coordinate singularity while for the present sol ution the singularity is a true singularity. It is speculated that thi s solution may give a confinement mechanism for non-Abelian gauge theo ries, since any particle which carries the SU(N + 1) charge would beco me permanently trapped inside the region r < r(0).