We investigate irreducible, 0(3) symmetric multiple-meron solutions to the classical SU(3) Yang-Mills equations in four-dimensional Euclidean space. The solution s have topological charge density equal to a sum of delta-functions with integer coefficients, and correspond to solutions of a system of two coupled singular elliptic equations. We prove the existence of twomeron solutions of the coupled system.
Infinite action solutions to the classical Yang-Mills equations in Euclidean space with topological charge density concentrated at points have been used by Glimm and Jaffe [1], and Callen et at.
[2] in models for quark confinement. The first such meron solution was found by deAlfaro et al.
[3] and was generalized to multiple merons on a line by Glimm and Jaffe [4]. Merons have only been studied in an SU(2) gauge theory, which can, of course, be embedded in the SU(3) theory believed to describe strong interactions. In this paper, we use the 0(3) symmetric ansatz of Bais and Weldon [5] to investigate SU(3) merons which do not arise from an embedding of SU(2) in SU(3). We call these irreducible.
We find some new phenomena in SU(3). Finding irreducible meron solutions is reduced to solving a pair of coupled elliptic equations, analogous to the equation r 2/Xr = ~k 3 -~ in the SU(2) case [4]. We prove that the equations have solutions corresponding to two-meron configurations. The charge density is a sum of unit delta-functions instead of the half delta-functions found in the SU(2) case. Although the word meron originated from fractional charges, we use it for integer charges as well because the solutions are similar to fractionally charged merons in other respects. They have regular, singular points and nonintegrable action.
Following Bais and Weldon [5], we define the following Hermitian, traceless matrices (a, b, l, m take values 1, 2, 3):
(La)lm = ielam, 2 ~ab~lm" (Qab )lm = 8alSbm + 6amSbl ---~ (1)