Vertex algebra–conformal net correspondence conjecture

Consider completely rational local conformal nets and unitary $C_2$-cofinite vertex operator algebras. Their finite-dimensional representations and modules carry unitary fusion-category structures, and both sides have corresponding characters.

Vertex algebra–conformal net correspondence conjecture. There is a bijective correspondence between completely rational local conformal nets and unitary $C_2$-cofinite vertex operator algebras. Under this correspondence, the unitary fusion categories of finite-dimensional representations and modules are equivalent, and the corresponding characters coincide.

This conjecture proposes a precise equivalence between the operator-algebraic and vertex-algebraic descriptions of rational two-dimensional conformal field theory. The source gives no resolution status.