Space-time supersymmetry of the covariant superstring

We explicitly derive the ghost oscillator contribution to the gauge covariant fermion emission vertex. This vertex is used to construct the space-time supersymmetry transformation laws which are shown to be an invariance of the free gauge covariant action of the superstring. We develop methods to deal with the quadratic exponentials which appear in the fermion emission vertex, in order to study the closure of the supersymmetry algebra. As a by-product, we complete the proof of the equivalence between the “old” and “new” formulations of the superstring.