Description
Classification of topological quantum field theories (or topological order in condensed matter) is one of the most fundamental problems in recent theoretical research (and experimental research to some extent). Recently, this problem has been analyzed by considering the domain wall problem between different TQFTs. Applying the correspondence between conformal field theory (CFT) and TQFT, the corresponding problem on the CFT side is the classification of the massless renormalization group (RG) between CFTs by Zamolodchikov or RG domain wall by Gaiotto. In this talk, we demonstrate that a general class of these domain wall problems can be solved by generalizing the method of integer spin simple current by Schellekens and Gato-Rivera. We provide general construction of unfamiliar (hopefully new) types of modular invariants and the resultant domain walls. Whereas the Moore-Seiberg data provides the ring isomorphism from one full CFT to the chiral CFT, our formalism provides ring homomorphism from one full CFT to other CFTs. Hence, our formalism is a natural extension of the Moore-Seiberg data. This talk is based on the recent preprint arXiv:2412.19577.
