Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects

Understand

This is the first of a series of papers discussing canonical aspects of the two-dimensional non-linear sigma model in the presence of conformal defects on the world-sheet in the framework of gerbe theory.

• In the paper, the basic tools of the state-space analysis are introduced, such as the symplectic structure on the state space of the sigma model and the pre-quantum bundle over it, and a relation between the defects and dualities of the sigma model is established.
• Also, a state-space description of the splitting-joining interaction of the string across the defect is presented, leading to an interpretation of the geometric data associated to junctions of defect lines in terms of intertwiners between the incoming and outgoing sectors of the theory in interaction.