Off-shell Invariants of Linearized 4D, 𝒩=2 Supergravity in the Harmonic Approach

Using the harmonic superspace approach, we construct, at the linearized level, 𝒩=2 supersymmetric curvatures generalizing scalar curvature, Ricci curvature and Weyl tensor. These supercurvatures are the building blocks of various linearized 4D, 𝒩=2 Einstein supergravity invariants. The supercurvatures involving the scalar and Ricci curvatures are analytic harmonic N=2 superfields, while the Weyl supertensor is a chiral 𝒩=2 superfield. As the basic distinguished feature of our construction, all these objects are expressed through the fundamental analytic gauge prepotentials h^++M, M= (αα̇, +α, +α̇, 5). The related characteristic features are the heavy use of harmonic derivatives and harmonic zero-curvature equations. On a number of instructive examples, we describe the component reduction of the superfield invariants constructed.