Strongly rational unitary vertex operator algebras and conformal nets
Every simple unitary strongly rational vertex operator algebra generates a completely rational conformal net. All its simple grading-restricted modules are unitarizable, its canonical fusion forms are positive, and the Carpi–Weiner–Xu functor gives a braided unitary tensor equivalence from its grading-restricted finite-length module category onto the finite-index sectors of the net. Gui's extension theorems then identify normalized irreducible finite-index local extensions of these nets with simple CFT-type conformal extensions of the vertex operator algebras.
Cite
@misc{OAI:Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026,
author = {{OpenAI}},
title = {{Strongly rational unitary vertex operator algebras and conformal nets}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026/paper.pdf}{OAI:Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026}},
year = {2026}
}