Three-dimensional gauge theories and monopoles Original Research Article

The Coulomb branch of N = 4 supersymmetric Yang-Mills gauge theories in d = 2 + 1 is studied. A direct connection between gauge theories and monopole moduli spaces is presented. It is proposed that the hyper-Kähler metric of supersymmetric N = 4 SU(N) Yang-Mills theory is given by the charge N centered moduli space of BPS monopoles in SU(2). The theory is compared to N = 2 supersymmetric Yang-Mills theory in four dimensions through compactification on a circle of the latter. It is found that rational maps are appropriate to this comparison. A BPS mass formula is also written for particles in three dimensions and strings in four dimensions.