A higher-dimensional generalization of the notion of vertex algebra

A higher-dimensional analogue of the notion of vertex algebra, called that of axiomatic Gn-vertex algebra, is formulated with Borcherdsʹ notion of G-vertex algebra as a motivation. Some examples are given and certain analogous duality properties are proved. 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 an axiomatic Gn-vertex algebra with W as a natural module.