Title: Monopoles and instantons on partially compactified<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>-branes
Abstract: Motivated by the recent $D$-brane constructions of world-volume monopoles and instantons, we study the supersymmetric SU$(N)$ Yang-Mills theory on ${S}^{1}\ifmmode\times\else\texttimes\fi{}{R}^{3+1}$, spontaneously broken by a Wilson loop. In addition to the usual $N\ensuremath{-}1$ fundamental monopoles, the $N$th 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.