The Conformal Hyperplet

We introduce a finite off-shell hypermultiplet with no off-shell central charge. This requires 192 + 192 degrees of freedom, all but 8 + 8 of which are auxiliary or gauge. In the absence of supergravity, the model has a saddle-point vacuum instability implying ghost-like propagators. These are cured by realizing the model superconformally, such that the erstwhile ghosts are realized as compensators. Gauge fixing these links the physical hypermultiplets to supergravity. This evokes the prospect of realizing N = 4 super-Yang-Mills theory off-shell.