Master Degree Project Presentation: Modularity Constraint on Topological Defect Lines in Two Dimensional Conformal Field Theories

Abstract: Topological defect lines (TDL) provide a framework for describing symmetries in two dimensional field theories, including a description of generalized symmetries, such as topological interfaces between theories, in addition to being the model for symmetry categories, generalizing the notion of symmetry groups. In this presentation I aim to give an introduction to TDL:s in compact, local, unitary two dimensional conformal field theories (CFT). Starting from the foundations of 2d-CFT, definitions and properties of TDL:s will be introduced, followed by a discussion on their mathematical structure and relation to fusion categories. Furthermore, using modular invariance of minimal 2d CFT:s, the modular bootstrap equation is derived, which constraints all possible TDL:s on a given minimal model. The application of this framework is demonstrated in practice with the Ising model, where we recover among others the Kramers–Wannier duality as a TDL.