Vertex Operator Superalgebras and the Majorana Fermion

Abstract

An introduction to vertex superalgebras and vertex operator superalgebras, with the free Majorana fermion as a worked example. The note develops signed identities, normal ordering, the Clifford realization, and the relation to the Ising VOA. Wick’s theorem gives Pfaffian formulas for vacuum correlation functions and for amplitudes with specified local coordinates. Regularized contractions encode descendant transformations and lead to efficient finite-matrix calculations. Further properties and computations are presented as exercises.