Conformal nets from minimal W-algebras

Fuente: arXiv
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Main Authors: Carpi, Sebastiano, Gaudio, Tiziano
Format: Preprint
Published: 2025
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author Carpi, Sebastiano
Gaudio, Tiziano
author_facet Carpi, Sebastiano
Gaudio, Tiziano
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_04270
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Conformal nets from minimal W-algebras
Carpi, Sebastiano
Gaudio, Tiziano
Mathematical Physics
High Energy Physics - Theory
Operator Algebras
Quantum Algebra
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.
title Conformal nets from minimal W-algebras
topic Mathematical Physics
High Energy Physics - Theory
Operator Algebras
Quantum Algebra
url https://arxiv.org/abs/2506.04270