We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure which associates to every strongly local vertex operator algebra V a conformal net A_V acting on the Hilbert space completion of V and prove that the isomorphism class of A_V does not depend on the choice of the scalar product on V. We show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W\mapsto A_W gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of A_V. Many known examples of vertex operator algebras such as the unitary Virasoro vertex operator algebras, the unitary affine Lie algebras vertex operator algebras, the known c=1 unitary vertex operator algebras, the moonshine vertex operator algebra, toge 查看全文>>