Holomorphic vertex operator algebra unitarity conjecture

A holomorphic VOA is a vertex operator algebra whose only irreducible module is itself. A VOA is unitary if it admits the required positive-definite invariant Hermitian structure.

Holomorphic VOA unitarity conjecture. Every holomorphic VOA is unitary.

All holomorphic VOAs with central charge at most $24$ discussed in the source are known to be unitary, as are the standard lattice and orbifold examples at higher central charge. The statement remains an empirical conjecture in general.