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W-algebras as conformal extensions of affine VOAs

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arxiv 2508.18889 v2 pith:FJXOQNLW submitted 2025-08-26 math.QA hep-thmath-phmath.MPmath.RT

W-algebras as conformal extensions of affine VOAs

Dra\v{z}en Adamovi\'c , Tomoyuki Arakawa , Thomas Creutzig , Andrew R. Linshaw , Anne Moreau , Pierluigi M\"oseneder Frajria , Paolo Papi This is my paper
classification math.QA hep-thmath-phmath.MPmath.RT
keywords vertexaffinew-algebrasconformalcriterionalgebrascollapseexamples
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We provide a criterion for a vertex operator superalgebra homomorphism from an affine vertex algebra to another vertex superalgebra to be conformal, and an additional criterion that guarantees that this homomorphism is surjective. This situation is applied to W-algebras and W-superalgebras and we list all cases where our criterion applies. This gives many new examples of W-algebras that collapse to affine vertex algebras or are conformal extensions. In particular, we provide many examples of simple W-algebras at non-admissible levels that collapse to admissible level affine vertex algebras.

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Cited by 2 Pith papers

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