Vertex Operator Algebra

Vertex Algebra

A vertex algebra is a collection of data:

1. A vector space (usually over ), called the state space.
2. An element , called the vacuum vector.
3. An endomorphism , called the translation operator.
4. A map , where denotes the space of formal Laurent series in with coefficients in . This map is called the state-field correspondence.

These data must satisfy the following axioms:

1. Vacuum Axiom: and .
2. Translation Axiom: and .
3. Locality Axiom: For all , there exists an integer such that in .