{"id":"hexagon/2611.00034","pdf":"https://hexagonmath.org/pdf/2611.00034v1","url":"https://hexagonmath.org/abs/2611.00034v1","tags":["msc:46L37","msc:81T40","msc:17B69","msc:18M20","Drinfeld center","Haagerup subfactor","Lagrangian algebra","conformal net","generalized orbifold","vertex operator algebra"],"score":0,"title":"Haagerup symmetries of the $E_8$ theory and conformal nets at central charge eight","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Cédric ARHANCET"],"reviews":0,"subject":"math.QA","summary":"A Haagerup algebra is a positive strongly rational vertex operator algebra $U$ of central charge eight with $\\Rep(U)$ braided equivalent to the Drinfeld center $Z(\\cal H_3)$ of the Haagerup fusion category. Such an algebra has been proposed by Jiao, with a computer-assisted proof, and announced by Riesen and by Huang. We show that $U$ has exactly three holomorphic extensions, each isomorphic to $V_{E_8}$, and that the categories of modules over the corresponding Lagrangian algebras are the three Haagerup fusion categories of Grossman and Snyder. The extensions attached to $\\cal H_2$ and…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}