The converse conjecture for irreducible graded-local conformal nets

Let A\mathcal{A} be an irreducible graded-local conformal net, meaning a graded-local conformal net satisfying the irreducibility condition. Converse conformal-net conjecture. For every irreducible graded-local conformal net A\mathcal{A}, there exists a simple strongly graded-local unitary vertex operator superalgebra VV such that

A=AV.\mathcal{A}=\mathcal{A}_V.

This is the conformal-net-to-VOSA direction of the proposed correspondence. The source does not state a resolution.

Sources & referencesView supporting material

Primary source

Sebastiano Carpi, Tiziano Gaudio and Robin Hillier, “From vertex operator superalgebras to graded-local conformal nets and back”, arXiv:2304.14263 (2025).

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