Vertex Operator Algebra - Virasoro Vertex Operator Algebra Example

Virasoro Vertex Operator Algebra Example

The Virasoro vertex operator algebra is a conformal vertex algebra. It is defined as follows:

With L(z) defined as above. So we have and with and . We see that this satisfies the axioms of a vertex algebra and includes a representation of the Virasoro algebra. The fact that the Virasoro field L(z) is local can be deduced from the formula for its self-commutator:

where c is central charge.