2025/12/09 by Jan Albert, Albert, Jan, Yamato Honda +5
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2512.08225
We suggest that the chiral (\mathfrake8)1 theory -- in many senses the simplest VOA -- may have Haagerup symmetry Hi for i=1,2,3. Likewise, we suggest that the non-chiral (E8)1 WZW model may have Hi × Hi^\textrmop symmetry, and that gauging the diagonal symmetry gives a c=8 theory with Z(H3) symmetry, which is the theory predicted in \citeEvans:2010yr. Along the way, we show that (E8)1 also has a Fib × Fibop symmetry, and that gauging the diagonal symmetry gives the (G2)1 × (F4)1 WZW model, explaining the well-known conformal embedding (G2)1 × (F4)1 ⊂ (E8)1. Finally, we suggest a relation to theories with H3 symmetry at c=2,6, complimenting the discussion with new modular bootstrap results.