  According to the proposal of Hanany and Witten, Coulomb branches of N=4 SU(n)
gauge theories in three dimensions are isometric to moduli spaces of BPS
monopoles. We generalize this proposal to gauge theories with matter, which
allows us to describe the metrics on their spaces of vacua by means of the
hyperk\"ahler quotient construction. To check the identification of moduli
spaces a comparison is made with field theory predictions. For SU(2) theory
with k fundamental hypermultiplets the Coulomb branch is expected to be the D_k
ALF gravitational instanton, so our results lead to a construction of such
spaces. In the special case of SU(2) theory with four or fewer fundamental
hypermultiplets we calculate the complex structures on the moduli spaces and
compare them with field-theoretical results. We also discuss some puzzles with
brane realizations of three-dimensional N=4 theories.

High Energy Physics - Theory