N-point locality for vertex operators: Normal ordered products, operator product expansions, twisted vertex algebras

In this paper we study fields satisfying N-point locality and their properties. We obtain residue formulae for N-point local fields in terms of derivatives of delta functions and Bell polynomials. We introduce the notion of the space of descendants of N-point local fields which includes normal ordered products and coefficients of operator product expansions. We show that examples of N-point local fields include the vertex operators generating the boson-fermion correspondences of types B, C and D-A. We apply the normal ordered products of these vertex operators to the setting of the representation theory of the double-infinite rank Lie algebras b∞, c∞, d∞. Finally, we show that the field theory generated by N-point local fields and their descendants has a structure of a twisted vertex algebra.