Light-cone superspace and the ultraviolet finiteness of the N=4 model

Superspace in the light-cone frame takes a simple form. No auxiliary fields are necessary, and application to extended supersymmetries is straightforward. It is shown that the N=4 model, in a certain form of the light-cone gauge, is completely free of ultraviolet divergences in any order of perturbation theory. It follows that the β-function vanishes in any gauge, to all orders of perturbation theory. Our method differs from the conventional method in that we use only half the number of θ's as there are supersymmetry operators. All fields are unconstrained and independent of the $\text{θ}\text{'}\text{s}$.