D-branes, Monopoles and Nahm Equations

TL;DR

This paper explores the relationship between D-branes, monopoles, and Nahm equations within super Yang-Mills theory, revealing how 1-brane bound states correspond to monopole moduli spaces and generalizing to higher gauge groups.

Contribution

It demonstrates a novel correspondence between 1-brane bound states and monopole solutions, extending the ADHMN construction to arbitrary SU(n) gauge groups.

Findings

Identification of super-symmetric ground states with monopole moduli space

Construction of monopole gauge fields via 1-brane quantum mechanics

Generalization to SU(n) monopoles for n>2

Abstract

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 super-symmetric 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 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 $n>2$.