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

Abstract

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.

62 pages, 7 tables, 1 figure. Several typos corrected. References updated

References in corpus (7)

• Braided tensor categories and extensions of vertex operator algebras
• Conformal Field Theories with Sporadic Group Symmetry
• Schellekens' List and the Very Strange Formula
• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• On classification of extremal non-holomorphic conformal field theories

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