An order-five Haagerup--Izumi vertex operator algebra at central charge eight
We construct an explicit unitary strongly rational vertex operator algebra $U$ of central charge eight inside $V_{A_4\oplus A_4}$ and identify $Rep(U)$ with the Drinfeld center of the positive order-five Haagerup--Izumi category. The construction adjoins one algebraic weight-two field to a diagonal affine $\mathfrak{sl}_2$ at level forty and the ambient conformal vector. Exact finite lattice identities imply strong generation and $C_2$-cofiniteness. A finite integral order in the actual Zhu algebra descends semisimplicity from a $1590$-dimensional upper presentation over $\mathbb F_{10069}$.…
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