Conjecture on the correspondence between rational conformal nets and vertex operator algebras

A completely rational local conformal net is a local conformal net with finite representation theory in the sense used in the source, and a simple unitary $C_2$-cofinite vertex operator algebra is a simple unitary vertex operator algebra satisfying $C_2$-cofiniteness. Characters are traces of $q^{L_0-c/24}$ when they converge. Correspondence conjecture. There is a bijective correspondence between completely rational local conformal nets and simple unitary $C_2$-cofinite vertex operator algebras; the finite-dimensional representation categories and the corresponding module categories are equivalent as tensor categories, and the characters of irreducible objects coincide. The conjecture proposes a fundamental equivalence between operator-algebraic conformal nets and vertex operator algebras, including their representation theories; the source gives no resolution.