Commutant of ${\mathcal{L}}_{{\widehat{\mathfrak{sl}}}_2}(4,0)$ in the cyclic permutation orbifold of ${\mathcal{L}}_{{\widehat{\mathfrak{sl}}}_2}(1,0{)}^{\otimes 4}$

Abstract

We study the commutant of the vertex operator algebra ${\mathcal{L}}_{{\widehat{\mathfrak{sl}}}_2}(4,0)$ in the cyclic permutation orbifold model $({\mathcal{L}}_{{\widehat{\mathfrak{sl}}}_2}(1,0{)}^{\otimes 4}{)}^{\tau }$ with $\tau =(1234)$. It is shown that the commutant is isomorphic to a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-orbifold model of a tensor product of two lattice type vertex operator algebras of rank one.

13 pages, no figure

References in corpus (1)

• Zhu's algebra, C_2-algebra and C_2-cofiniteness of parafermion vertex operator algebras