OPE-Algebras and their Modules

Abstract

Vertex algebras formalize the subalgebra of holomorphic fields of a conformal field theory. OPE-algebras were proposed as a generalization of vertex algebras that formalizes the algebra of all fields of a conformal field theory. We prove some basic results about them: The state-field correspondence is an OPE-algebra isomorphism and Dong's lemma and the existence theorem hold for multiply local OPE-algebras; locality implies skew-symmetry; if skew-symmetry holds then duality implies locality for modules and they are equivalent for algebras. We define modules over OPE-algebras.