SINGULAR MONOPOLES AND SUPERSYMMETRIC GAUGE-THEORIES IN 3 DIMENSIONS

According to the proposal of Hanany and Witten, Coulomb branches of N = 4 SU(n) gauge theories in three dimensions are isometric to moduli s paces of BPS monopoles, We generalize this proposal to gauge theories with matter, which allows us to describe the metrics on their spaces o f vacua by means of the hyper-Kahler quotient construction. To check t he identification of moduli spaces a comparison is made with field the ory predictions, For SU(2) theory with k fundamental hypermultiplets t he Coulomb branch is expected to be the D-k ALF gravitational instanto n, so our results lead to a construction of such spaces. In the specia l case of SU(2) theory with four or fewer fundamental hypermultiplets we calculate the complex structures on the moduli spaces and compare t hem with field-theoretical results. We also discuss some puzzles with brane realizations of three-dimensional N = 4 theories. (C) 1998 Elsev ier Science B.V.