O(3)-symmetric merons inSU(N)gauge theory

Abstract

We investigate nonreducible O(3)-symmetric meron solutions to classical $\mathrm{SU}(N+1)$ Yang-Mills theory in four-dimensional Euclidean space. For even $N$ the solutions have topological charge densities equal to a sum of $\ensuremath{\delta}$ functions with integer coefficients while for odd $N(Ng1)$ these coefficients can be both integer and half-integer. In all cases they correspond to solutions of a system of $N$ coupled singular elliptic equations. We discuss the existence of two-meron solutions of this system and for $N=3,4$ give some numerical solutions.