Haagerup conformal field theory at central charge eight

Abstract

We construct a chiral algebra $U$ of central charge eight inside the lattice vertex operator algebra $V_{E_6\oplus A_2}$. It is generated by two commuting affine $\mathfrak{sl}_2$ current algebras at levels $1$ and $39$, the stress tensor of the lattice theory, and a single weight-two field built from three lattice exponentials. We announce that $U$ is strongly rational and completely unitary, and that $Rep(U)$ is equivalent, as a unitary ribbon category, to the Drinfeld center $Z(\mathcal{H}_3)$ of the Haagerup fusion category $\mathcal{H}_3$. Its characters are the $γ=0$ Evans--Gannon vector. From $U$ we obtain a diagonal full CFT, and also a holomorphic $E_8$ extension on which $\mathcal{H}_3$ acts by topological defects.