Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions

Details Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions

1997-11-19

arxiv.org/abs/hep-th/9711145v2

Nucl.Phys. B525 (1998) 215-234

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, LaTeX, 6 figures; exposition improved

Scientific paper

10.1016/S0550-3213(98)00341-1

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.

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