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

TL;DR

This paper classifies all two-primary, unitary RCFTs with central charge less than 25, identifying known theories and their cosets, and explicitly enumerates 123 theories, most of which are new, using a novel approach.

Contribution

The authors provide a complete classification of two-primary RCFTs with c<25, including explicit enumeration of new theories via cosets of holomorphic VOAs and existing MMS theories.

Findings

Identified all such RCFTs as MMS theories or their cosets.

Explicitly enumerated 123 theories, most being new.

Developed a general technique applicable to low central charge chiral algebra classification.

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.