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We investigate some of the properties of D-brane configurations which behave as BPS monopoles. The two D-brane configurations we will study are the enhançon and D-strings attached to D3-branes.We will start by investigating D3-branes wrapped on a K3 manifold, which are known as enhançons. They look like regions of enhanced gauge symmetry in the directions transverse to the branes, and therefore behave as BPS monopoles. We calculate the metric on moduli space for n enhançons, following the methods used by Ferrell and Eardley for black holes. We expect the result to be the higher-dimensional generalisation of the Taub-NUT metric, which is the metric on moduli space for n BPS monopoles. Next we will study D-strings attached to D3-branes; the ends of the D-strings behave as BPS monopoles of the world volume gauge theory living on the D3-branes. In fact the D-string/D3-brane system is a physical realisation of the ADHMN construction for BPS monopoles. We aim to test this correspondence by calculating the energy radiated during D-string scattering, working with the non-Abelian Born-Infeld action for D-strings. We will then compare our result to the equivalent monopole calculation of Manton and Samols.

Bibliography : leaves 117-120 / vi, 120 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992

Bibliography : p. 105-111 / xi, 111 p. : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992

This thesis is mainly concerned with the study of hypersymplectic structures in gauge theory. These structures arise via applications of the hypersymplectic quotient construction to the action of the gauge group on certain spaces of connections and Higgs fields. Motivated by Kobayashi-Hitchin correspondences in the case of hyperkähler moduli spaces, we first study the relationship between hypersymplectic, complex and paracomplex quotients in the spirit of Kirwan's work relating Kähler quotients to GIT quotients. We then study dimensional reductions of the ASD equations on $mathbb R^{2,2}$. We discuss a version of twistor theory for hypersymplectic manifolds, which we use to put the ASD equations into Lax form. Next, we study Schmid's equations from the viewpoint of hypersymplectic quotients and examine the local product structure of the moduli space. Then we turn towards the integrability aspects of this system. We deduce various properties of the spectral curve associated to a solution and provide explicit solutions with cyclic symmetry. Hitchin's harmonic map equations are the split signature analogue of the self-duality equations on a Riemann surface, in which case it is known that there is a smooth hyperkähler moduli space. In the case at hand, we cannot expect to obtain a globally well-behaved moduli space. However, we are able to construct a smooth open set of solutions with small Higgs field, on which we then analyse the hypersymplectic geometry. In particular, we exhibit the local product structures and the family of complex structures. This is done by interpreting the equations as describing certain geodesics on the moduli space of unitary connections. Using this picture we relate the degeneracy locus to geodesics with conjugate endpoints. Finally, we present a split signature version of the ADHM construction for so-called split signature instantons on $S^2 imes S^2$, which can be given an interpretation as a hypersymplectic quotient.