Family 280Mathematical physicsNo LeanNot yet digested
Unitary vertex operator algebras and conformal nets
Proves the strongly rational case of the strong-locality conjecture: every simple unitary strongly rational complex vertex operator algebra generates a completely rational conformal net. Its simple modules are unitarizable, and its representation category agrees with the net’s finite-index sectors as a braided unitary tensor category.
Manuscripts in this family · 1
Strongly rational unitary vertex operator algebras and conformal nets
Sep 25, 2026·paper.pdf
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.