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arXiv · 2506.04270

Conformal nets from minimal W-algebras

Sebastiano Carpi·Tiziano Gaudio
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Abstract

We show the strong graded locality of all unitary minimal W-algebras, so that they give rise to irreducible graded-local conformal nets. Among these unitary vertex superalgebras, up to taking tensor products with free fermion vertex superalgebras, there are the unitary Virasoro vertex algebras (N=0) and the unitary N=1,2,3,4 super-Virasoro vertex superalgebras. Accordingly, we have a uniform construction that gives, besides the already known N=0,1,2 super-Virasoro nets, also the new N=3,4 super-Virasoro nets. All strongly rational unitary minimal W-algebras give rise to previously known completely rational graded-local conformal nets and we conjecture that the converse is also true. We prove this conjecture for all unitary W-algebras corresponding to the N=0,1,2,3,4 super-Virasoro vertex superalgebras.

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Sebastiano Carpi, Tiziano Gaudio. 2025-06-03. Conformal nets from minimal W-algebras. https://doi.org/10.1007/s00220-025-05468-2

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