Monopoles and instantons on partially compactifiedD-branes

Motivated by the recent D-brane constructions of world-volume monopoles and instantons, we study the supersymmetric SU$(N)$ Yang-Mills theory on S¹×R³⁺¹, spontaneously broken by a Wilson loop. In addition to the usual N-1 fundamental monopoles, the Nth Bogomol'nyi-Prasad-Sommerfield monopole appears from the Kaluza-Klein sector. When all N monopoles are present, net magnetic charge vanishes and the solution can be reinterpreted as a Wilson-loop instanton of unit Pontryagin number. The instanton-multimonopole moduli space is explicitly constructed, and seen to be identical to a Coulomb phase moduli space of a U(1)N gauge theory in $2+1$ dimensions related to Kronheimer's gauge theory of SU$(N)$-type. This extends the results by Intriligator and Seiberg to the finite couplings that, in the infrared limit of Kronheimer's theory, the Coulomb phase parametrizes a centered SU$(N)$ instanton. We also elaborate on the case of restored SU$(N)$ symmetry.