Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25

We classify all two-dimensional, unitary, rational conformal field theories with two primaries, central charge $$c<25$$ , and arbitrary Wronskian index. In mathematical parlance, we strongly regular vertex operator algebras (VOAs) exactly simple modules. find that any such theory is either one of the Mathur–Mukhi–Sen (MMS) or it a coset chiral algebra primary (also known as holomorphic VOA) by an MMS theory. By leveraging existing results on classification VOAs, are able to explicitly enumerate aforementioned cosets compute their characters. This leads 123 theories, most which new. emphasize our work bona fide RCFTs, not just Our techniques general, argue they offer promising strategy for classifying low beyond primaries.