N=2 supergravity in superspace: solution to the constraints and the invariant action

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Abstract
The authors develop the off-shell unconstrained formulation of N=2 Einstein supergravity in harmonic superspace. The elements of differential geometry are constructed in terms of the prepotentials (the analytic vielbeins of the harmonic covariant derivative D++). Thus, the authors find the solution to the constraints of the first off-shell version of the theory. A number of useful 'building blocks' with simple transformation properties are constructed from the prepotentials. They are used to obtain a density for the full supervolume of harmonic superspace. One can then write down the invariant action for this version of the theory. The proof of the invariance relies on the existence of a new 'hybrid' basis in harmonic superspace in which semi-chirality together with analyticity are manifest.

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