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 $\gamma =0$ 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.

arXiv comment11 pages. v2 adds bootstrap plots, citations, and a note