D-branes, monopoles and Nahm equations

We study the correspondence between IIb solitonic 1-branes and monopoles 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 between two separated 3-branes exhibits a family of supersymmetric ground states that can be identified with the ADHMN construction of the moduli space of SU(2) monopoles. This identification is supported by the construction 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 described by non-commuting matrix valued fields which develop poles at the boundary. Finally, the construction is generalized to SU(n) monopoles with arbitrary n > 2. (C) 1997 Elsevier Science B.V.