Towards a classification of fermionic rational conformal field theories

Abstract

Two-dimensional conformal field theories (CFTs) play an important role in modern theoretical physics. Among them, rational CFTs enjoy particularly nice properties and hence are amenable to a possible classification. In this talk, I will review some recent progress towards classifying Rational CFTs with fermions using the holomorphic modular bootstrap method, which is related to but different from the classification of super modular tensor categories (MTCs). As one of the main results, we successfully bootstrap theories with small number of characters, which already reveal interesting phenomena such as fermionization, SUSY enhancement and the moonshine of sporadic groups. Finally, partly inspired by the congruence property of MTC, we make use of the integrality of characters to improve our classification.