On certain higher dimensional analogues of vertex algebras

Abstract

A higher dimensional analogue of the notion of vertex algebra is formulated in terms of formal variable language with Borcherds' notion of $G$-vertex algebra as a motivation. Some examples are given and certain analogous duality properties are proved. Furthermore, it is proved that for any vector space $W$, any set of mutually local multi-variable vertex operators on $W$ in a certain canonical way generates a vertex algebra with $W$ as a natural module.