Vertex Operator Algebra - Monster Vertex Algebra

Monster Vertex Algebra

The monster vertex algebra is a conformal vertex operator derived from 26 dimensional bosonic string theory compactified on the hyper-torus induced by the Leech lattice and orbifolded by the two-element reflection group. It is denoted as V♮. It was used to prove the Monstrous moonshine conjectures.

In the string model the vectors a in Y(a,z) are the different states or vibrational modes of the string which correspond to different particles and polarisations and z is a point (or vertex) on the world sheet which corresponds to an ingoing or outgoing string. Hence why it is called a Vertex Algebra.