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Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics

We propose an explanation via string theory of the correspondence between the Coulomb branch of certain three-dimensional supersymmetric gauge theories and certain moduli spaces of magnetic monopoles. The same construction also gives an explanation, via $SL(2,\Z)$ duality of Type IIB superstrings, of the recently discovered ``mirror symmetry'' in three dimensions. New phase transitions in three dimensions as well as new infrared fixed points and even new coupling constants not present in the known Lagrangians are predicted from the string theory construction. An important role in the construction is played by a novel aspect of brane dynamics in which a third brane is created when two branes cross.