Quantized non-Abelian monopoles onS3

Abstract

A possible electric-magnetic duality suggests that the confinement of non-Abelian electric charges manifests itself as a perturbative quantum effect for the dual magnetic charges. Motivated by this possibility, we study vacuum fluctuations around a non-Abelian monopole-antimonopole pair treated as point objects with charges g={+-}n/2 (n=1,2,...), and placed on the antipodes of a three sphere of radius R. We explicitly find all the fluctuation modes by linearizing and solving the Yang-Mills equations about this background field on a three sphere. We recover, generalize, and extend earlier results, including those on the stability analysis of non-Abelian magnetic monopoles. We find that for g{>=}1 monopoles there is an unstable mode that tends to squeeze magnetic flux in the angular directions. We sum the vacuum energy contributions of the fluctuation modes for the g=1/2 case and find oscillatory dependence on the cutoff scale. Subject to certain assumptions, we find that the contribution of the fluctuation modes to the quantum zero-point energy grows as {approx}-R{sup -2/3} and hence decays more slowly than the classical -R{sup -1} Coulomb potential for large R. However, the growth of the zero-point energy does not agree with the linear growth expected if the monopoles are confined.