Commutant of $\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(4,0)$ in the   cyclic permutation orbifold of   $\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(1,0)^{\otimes 4}$
  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 $\tau=(1\,2\,3\,4)$. 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. 
Toshiyuki Abe, Hiromichi Yamada
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