# Curiosities above c = 24

## TL;DR

This paper explores the classification of two-character rational conformal field theories with a specific focus on the case where the parameter =6, introducing a new method based on cosets of meromorphic CFTs and constructing the first known theories beyond =2.

## Contribution

It proposes a novel classification approach for =6 RCFTs using cosets of meromorphic CFTs and constructs the first examples beyond =2.

## Key findings

- Classified =6 RCFTs with central charges between 24 and 32.
- Developed a coset-based classification method.
- Constructed the first known two-character RCFTs beyond =2.

## Abstract

Two-dimensional rational CFT are characterised by an integer $\ell$, related to the number of zeroes of the Wronskian of the characters. For two-character RCFT's with $\ell<6$ there is a finite number of theories and most of these are classified. Recently it has been shown that for $\ell \ge 6$ there are infinitely many admissible characters that could potentially describe CFT's. In this note we examine the $\ell=6$ case, whose central charges lie between 24 and 32, and propose a classification method based on cosets of meromorphic CFT's. We illustrate the method using theories on Kervaire lattices with complete root systems. In the process we construct the first known two-character RCFT's beyond $\ell=2$.