Abstract
This paper concludes the formulation of N=2 supergravity in harmonic superspace. The authors generalize the approach to include conformal supergravity. The superconformal group is then compensated by coupling to a Maxwell and various matter multiplets. All the previously known versions of N=2 Einstein supergravity are reproducible in this way. The authors give one example (with the non-linear multiplet as a compensator). Their main result is a new version of N=2 Einstein supergravity which involves an off-shell complex hypermultiplet with its infinitely many auxiliary fields. They believe this version to be fundamental.
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