Superconformal D-branes and moduli spaces

TL;DR

This thesis explores dualities between gauge theories via D-brane configurations and derives superconformal boundary conditions for open string models, revealing insights into D-brane geometries and string dualities.

Contribution

It establishes a duality between N=2 quiver and Seiberg-Witten theories through D-brane moduli spaces and derives the most general superconformal boundary conditions for nonlinear sigma models.

Findings

Identified an identity between moduli spaces of dual gauge theories.

Derived the most general local superconformal boundary conditions.

Analyzed boundary conditions in WZW models.

Abstract

This thesis first gives a background and review of the article hep-th/0102038, where we substantiated a conjectured duality between two a priori unrelated gauge theories, N=2 quiver theory and N=2 Seiberg-Witten theory. 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, the thesis gives a background and description of the analysis performed in the three articles hep-th/0111161, hep-th/0202069 and hep-th/0304013, 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.