Parafermion vertex operator algebras and W-algebras

Tomoyuki Arakawa; Ching Hung Lam; Hiromichi Yamada

paper

Parafermion vertex operator algebras and W-algebras

arXiv:1701.06229

Abstract

We prove the conjectual isomorphism between the level $k$ $s l_{2}$ -parafermion vertex operator algebra and the $(k + 1, k + 2)$ minimal series $W_{k}$ -algebra for all integers $k \geq 2$ . As a consequence, we obtain the conjectural isomorphism between the $(k + 1, k + 2)$ minimal series $W_{k}$ -algebra and the coset vertex operator algebra $S U (k)_{1} \otimes S U (k)_{1} / S U (k)_{2}$ .

24 pages

Cited by in corpus (1)

Representations of $Z_{2}$ -orbifold of the parafermion vertex operator algebra $K (s l_{2}, k)$