Conformal nets from minimal W-algebras
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.
Keywords
Cite
@article{arxiv.2506.04270,
title = {Conformal nets from minimal W-algebras},
author = {Sebastiano Carpi and Tiziano Gaudio},
journal= {arXiv preprint arXiv:2506.04270},
year = {2025}
}
Comments
39 pages, final author's version of the original article published in Communications in Mathematical Physics