Under the assumption that the R-filtration is weight-based, only the (3,q+4) minimal models of W3 algebras are compatible with graded unitarity from 4d SCFTs.
Mizoguchi,Determinant Formula and Unitarity for theW(3) Algebra,Phys
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Towards a classification of graded unitary ${\mathcal W}_3$ algebras
Under the assumption that the R-filtration is weight-based, only the (3,q+4) minimal models of W3 algebras are compatible with graded unitarity from 4d SCFTs.