Superconformal D-branes and moduli spaces

Sammanfattning: The on-going quest for a single theory that describes all the forces of nature has led to the discovery of string theory. This is the only known theory that successfully unifies gravity with the electroweak and strong forces. It postulates that the fundamental building blocks of nature are strings, and that all particles arise as different excitations of strings. This theory is still poorly understood, especially at strong coupling, but progress is being made all the time. One breakthrough came with the discovery of extended objects called D-branes, which have proved crucial in probing the strong-coupling regime. They are instrumental in realising dualities (equivalences) between different limits of string theory. This thesis is concerned with dualities and D-branes. First, it gives a background and review of the first article, where we substantiated a conjectured duality between two a priori unrelated gauge theories. These gauge theories have different realisations as the worldvolume theories on different D-brane configurations. We showed that there is an identity between the spaces of vacua (moduli spaces) arising in the two theories, which suggests that the corresponding string theory pictures are dual. Second, we give a background and description of the analysis performed in the remaining three articles, where we derived the most general, local, superconformal boundary conditions of the two-dimensional nonlinear sigma model. This model describes the dynamics of open strings, and the boundary conditions dictate the geometry of D-branes. In the last article we studied these boundary conditions for the special case of WZW models.