Two-monopole systems and the formation of non-Abelian clouds

Abstract

We study the energy density of two distinct fundamental monopoles in SU͑3͒ and Sp͑4͒ theories with an arbitrary mass ratio. Several special limits of the general result are checked and verified. Based on the analytic expression of energy density the coefficient of the internal part of the moduli space metric is computed, which gives it a nice ''mechanical'' interpretation. We then investigate the interaction energy density for both cases. By analyzing the contour of the zero interaction energy density we propose a detailed picture of what happens when one gets close to the massless limit. The study of the interaction energy density also sheds light on the formation of the non-Abelian cloud. ͓S0556-2821͑98͒04822-X͔ PACS number͑s͒: 11.27.ϩd, 11.15.Ϫq, 14.80.Hv II. NAHM'S FORMALISM FOR THE ENERGY DENSITYAs was used in many papers, Nahm's formalism has proved to be a powerful tool in calculating many aspects of monopoles. This method is an analogue of the Atiyah-Drinfeld-Hitchin-Manin ͑ADHM͒ construction used in instanton physics ͓9͔ and was first proposed by Nahm ͓10͔. Recently Nahm's formalism has been generalized to deal with calorons ͑periodic instantons͒ ͓11,12͔, and we will use some of the results developed in those works.Consider the SU͑N͒ Yang-Mills-Higgs system. Assuming the asymptotic Higgs field along a given direction to be ϱ *

Magnetic monopole dynamics, supersymmetry, and duality

“…If we had started out with the (1, 1) solutions of maximally broken SU(3), we would have obtained the same flat R 4 relative moduli space in the massless limit. However, as we have already noted, the classical (1, 1) solutions do not behave smoothly in this limit: the massless monopole expands without bound [160], and the (1, [1]) solution that is obtained in the limit is gauge equivalent to the (1, [0]) solution which, having only a single monopole, has no relative moduli space.…”

“…In this case, which does not satisfy Eq. (6.1.5), the growth of the lighter monopole is not cut off by the presence of the massive monopole, but instead continues until, in the massless limit, the monopole has infinite radius but is essentially indistinguishable from the vacuum [160]. Indeed, the limiting (1, [1]) solution that one obtains in this fashion is gauge-equivalent to the (1, [0]) massive monopole.…”

“…However, the growth of this would-be massless monopole is affected by its nonlinear coupling to the other monopole. When the radius of the lighter monopole becomes of order R, this interaction prevents any further increase in size, and the monopole evolves into the non-Abelian cloud [160].…”

Interactions of massless monopole clouds

“…One finds that an isolated fundamental monopole solution goes over to the vacuum solution as it becomes massless. The behavior of multimonopole solutions is more complex [3]. If the total magnetic charge remains purely Abelian, then the solution rapidly approaches its limiting form once the inverse of the smallest monopole mass becomes larger than the separations of the component monopoles.…”

Massless monopole clouds and electric–magnetic duality

“…In addition to the usual moduli of positions and U(1) phases of the massive monopoles, there are also ones describing the unbroken non-Abelian gauge group, as well as the sizes or shapes of the clouds. There have been many extended studies on both the BPS configurations [9][10][11][12][13][14][15] and the low energy classical dynamics [16][17][18] of such clouds. However, it remains unclear how such configurations and their properties should be properly placed in the context of the electric-magnetic duality of the N = 4 theory and how it may be related to the properties of the QCD confinement.…”