This study reveals the isomorphism of minimal W-algebra in soN, indicating strong rationality in even cases.
For N ∈ Z≥ 7 we show that the simple minimal W-algebra of soN at level minus one is isomorphic to the even subalgebra of the tensor product of the simple affine vertex superalgebra of osp1|2 at level N-6/2 with $N-4$ free fermions. In particular when N is even this minimal W-algebra is strongly rational as conjectured by Arakawa-Moreau.
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Creutzig et al. (2025) studied this question.
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