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Haagerup Symmetry in (E_{8})_{1}?

Jan Albert1, Yamato Honda2, Justin Kaidi2,3,4

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The chiral (e8)1 theory may possess Haagerup symmetry. Gauging symmetries in related models reveals new conformal field theories and explains known embeddings, advancing vertex operator algebra research.

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Area of Science:

  • Theoretical physics
  • Conformal field theory
  • Vertex operator algebras

Background:

  • The (E8)1 theory is a fundamental vertex operator algebra.
  • Understanding symmetries in conformal field theories is crucial for classification and prediction.
  • Previous work predicted specific theories with Z(H3) symmetry.

Purpose of the Study:

  • To explore potential Haagerup symmetries in the chiral (E8)1 theory.
  • To investigate symmetries in the nonchiral (E8)1 Wess-Zumino-Witten model.
  • To explain conformal embeddings and relate theories with specific central charges.

Main Methods:

  • Analysis of vertex operator algebra symmetries.
  • Gauging diagonal symmetries in Wess-Zumino-Witten models.
  • Application of modular bootstrap techniques.
  • Investigation of conformal embeddings.

Main Results:

  • Suggested Haagerup symmetry (Hi) for the chiral (E8)1 theory.
  • Proposed Hi × Hi^op symmetry for the nonchiral (E8)1 WZW model.
  • Demonstrated that gauging diagonal symmetry yields a c=8 theory with Z(H3) symmetry.
  • Showed (E8)1 possesses Fib × Fib^op symmetry, leading to the (G2)1 × (F4)1 WZW model upon gauging.
  • Explained the conformal embedding (G2)1 × (F4)1 ⊂ (E8)1.
  • Suggested connections to theories with H3 symmetry at c=2, 6.

Conclusions:

  • The findings provide new insights into the symmetries of the (E8)1 theory and related models.
  • The study explains known conformal embeddings and predicts new theories.
  • New modular bootstrap results complement the theoretical analysis.