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

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arxiv 2208.05486 v3 pith:Y5QAGO3I submitted 2022-08-10 hep-th math.QAmath.RT

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

classification hep-th math.QAmath.RT
keywords centralchargemathsfclassificationprimariestheoriesalgebrascharacters
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 classify all strongly regular vertex operator algebras (VOAs) with central charge $c<25$ and exactly two simple modules. We find that any such theory is either one of the Mathur-Mukhi-Sen (MMS) theories $\mathsf{A}_{1,1}$, $\mathsf{G}_{2,1}$, $\mathsf{F}_{4,1}$, or $\mathsf{E}_{7,1}$, or it is a coset of a chiral algebra with one primary operator (also known as a holomorphic VOA) by such an MMS theory. By leveraging existing results on the classification of holomorphic VOAs, we are able to explicitly enumerate all of the aforementioned cosets and compute their characters. This leads to 123 theories, most of which are new. We emphasize that our work is a bona fide classification of RCFTs, not just of characters. Our techniques are general, and we argue that they offer a promising strategy for classifying chiral algebras with low central charge beyond two primaries.

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