October 20, 2025Open Access

Minimal W-algebras of soN at level minus one

TCThomas CreutzigFriedrich-Alexander-Universität Erlangen-Nürnberg JFJustine FasquelCentre National de la Recherche Scientifique VKVladimir KovalchukUniversity of Denver

Key Points

The simple minimal W-algebra of soN at level minus one is isomorphic to a specific tensor product.
For even N, the minimal W-algebra is strongly rational, consistent with Arakawa-Moreau's conjecture.
The algebra comprises the even subalgebra of a tensor product involving the simple affine vertex superalgebra.
This confirms certain properties of minimal W-algebras for N greater than or equal to seven.

Abstract

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-62 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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