Abstract:

The study of the gapless edges of 2+1D topological orders demands a mathematical theory of 1+1D conformal field theories far beyond those covered in the famous yellow book (Di Francesco et al. 1997). Some crucial parts of this theory were developed after 2000. In this talk and its sequels, we will review the mathematical theory of 2D rational conformal field theories (RCFT) based on the representation theory of vertex operator algebras. We will focus on the classification of open-closed RCFT’s and open-closed duality. After this preparation, we will explain the mathematical theory of the gapless edges of 2+1D topological orders developed jointly with Hao Zheng.