Haagerup Symmetry in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>8</mml:mn> </mml:mrow> </mml:msub>

We suggest that the chiral (e_{8})_{1} theory-in many senses the simplest vertex operator algebra-may have Haagerup symmetry H_{i} for i=1, 2, 3. Likewise, we suggest that the nonchiral (E_{8})_{1} Wess-Zumino-Witten model may have H_{i}×H_{i}^{op} symmetry, and that gauging the diagonal symmetry gives a c=8 theory with Z(H_{3}) symmetry, which is the theory predicted in Evans and Gannon [Commun. Math. Phys. 307, 463 (2011)CMPHAY0010-361610.1007/s00220-011-1329-3]. Along the way, we show that (E_{8})_{1} also has a Fib×Fib^{op} symmetry, and that gauging the diagonal symmetry gives the (G_{2})_{1}×(F_{4})_{1} Wess-Zumino-Witten model, explaining the well-known conformal embedding (G_{2})_{1}×(F_{4})_{1}⊂(E_{8})_{1}. Finally, we suggest a relation to theories with H_{3} symmetry at c=2, 6, complimenting the discussion with new modular bootstrap results.