Irregular vertex algebras

Abstract

We introduce the notion of irregular vertex (operator) algebras. The irregular versions of fundamental properties, such as Goddard uniqueness theorem, associativity, and operator product expansions are formulated and proved.We also give some elementary examples of irregular vertex operator algebras. Contents 1. Introduction 1 2. Coherent state modules 8 3. Irregular vertex operator algebras 13 4. Associativity and operator product expansions 20 5. Irregular Heisenberg vertex operator algebras 25 6. Irregular Virasoro vertex operator algebras 32 Concluding remarks 36 References 36