Boundary states in conformal field theory

Abstract: This licentiate thesis discusses boundary states in conformal field theories related to WZW (Wess-Zumino-Witten) models. These models are used as building blocks to describe the compact extra dimensions of certain string theories. The focus of the first chapter is to give a flavor of conformal field theory. The second chapter treats WZW- and related models. Such models can be described from a geometric perspective, or from an algebraic perspective. The discussion in this text is mostly from the latter perspective, but some attention is being paid to the relation between the two approaches. The third and final chapter deals with boundary states in WZW- and related models. The physical application aimed at is the description of D-branes in string theory, subsets of space-time to which string end points are confined. The relation between the concept of D-branes and the concept of boundary states is not direct, as discussed in the beginning of chapter 3. It turns out that the boundary states, if interpreted in geometric language as D-branes, in many cases are ''smeared''. This was known already to Felder et al, together with the fact that 0- dimensional branes in WZW models do not exist. The first new result in this thesis is a concrete argument for the latter statement. An important class of models that are related to WZW models are the coset models. These are introduced in chapter 2, and some novel results on the geometric interpretation of their boundary states as D- branes can be found in chapter 3. Apart from the coset models, there are also geometric orbifold models related to WZW- models. Concrete examples of such models are the Lens space models, on which an article was published in collaboration with Pedro Bordalo. Results from this paper can be found in the final two sections of chapter 3.