SciPost Phys. 6, 053 (2019) ·
published 6 May 2019

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Twodimensional rational CFT are characterised by an integer $\ell$, related
to the number of zeroes of the Wronskian of the characters. For twocharacter
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
twocharacter RCFT's beyond $\ell=2$.