Monopole solutions in classical SU(3) gauge theory.

Abstract

We consider monopole solutions in nonabelian SU(3) Yang – Mills – Higgs gauge theory. Using spherically symmetric ansatz for SU(3) gauge and scalar fields, we obtain Yang – Mills – Higgs equations as well as Bogomol’nyi equations. We show that statically Yang – Mills – Higgs equations follow from Bogomol’nyi equations. Bogomol’nyi equation system comprising four first-order differential equations was transformed into the system consisting of two second-order differential equations, and two algebraic equations. By Taylor-expanding equations, we obtain approximate analytical solutions at the centre of the monopole. We also consider asymptotic behavior of the monopole solutions. Complete solution is obtained numerically. We show that the monopole solutions depend on two parameters, and we obtain the dependence of the energy of the monopole on these parameters. On the parameters plane we obtain a curve that separates regular and singular solutions.