We investigate the self-dual Yang-Mills gauge configurations on R 3 × S 1 when the gauge symmetry SU(2) is broken to U(1) by the Wilson loop. We construct the explicit field configuration for a single instanton by the Nahm method and show that an instanton is composed of two self-dual monopoles of opposite magnetic charge. We normalize the moduli space metric of an instanton and study various limits of the field configuration and its moduli space metric.

We compute the exact finite temperature effective action in a 0+1-dimensional field theory containing a topological Chern-Simons term, which has many features in common with 2+1-dimensional Chern-Simons theories.This exact result explains the origin and meaning of puzzling temperature dependent coefficients found in various naive perturbative computations in the higher dimensional models.There are many examples in physics in which the classical Lagrange density contains a term that is not strictly invariant under a certain transformation (for example, a 'large' gauge transformation), but the classical action changes by a constant that takes discrete values associated with the 'winding number' of the transformation. For such a system the

Starting from Nahm's equations, we explore Bogomol'nyi-Prasad-Sommerfield ͑BPS͒ magnetic monopoles in the Yang-Mills-Higgs theory of the gauge group Sp͑4͒, which is broken to SU(2)ϫU(1). There exists a family of BPS field configurations with a purely Abelian magnetic charge that describes two identical massive monopoles and one massless monopole. We construct the field configurations with axial symmetry by employing the Atiyah-Drinfeld-Hitchin-Mannin-Nahm construction and find the explicit expression of the metrics for the 12-dimensional moduli space of Nahm data and its submanifolds. ͓S0556-2821͑98͒01408-8͔

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 *