Three Dimensional Gauge Theories and Monopoles

Details Three Dimensional Gauge Theories and Monopoles Three Dimensional Gauge Theories and Monopoles

1996-08-15

arxiv.org/abs/hep-th/9608105v2

Nucl.Phys. B489 (1997) 223-244

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1016/S0550-3213(97)00036-9

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-K\"ahler 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.

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