D-BRANES, MONOPOLES AND NAHM EQUATIONS

We study the correspondence between IIb solitonic 1-branes and monopol es in the context of the 3-brane realization of D = 4 N = 4 super Yang -Mills theory. We show that a bound state of 1-branes stretching betwe en two separated 3-branes exhibits a family of supersymmetric ground s tates that can be identified with the ADHMN construction of the moduli space of SU(2) monopoles. This identification is supported by the con struction of the monopole gauge field as a space-time coupling in the quantum mechanical effective action of a 1-brane used as a probe. The analysis also reveals an intriguing new aspect of the 1-brane theory: the transverse oscillations of the 1-branes in the ground states are d escribed by non-commuting matrix valued fields which develop poles at the boundary. Finally, the construction is generalized to SU(n) monopo les with arbitrary n > 2. (C) 1997 Elsevier Science B.V.