Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach

Abstract

Using the harmonic superspace approach, we construct, at the linearized level, $\mathcal{N}=2$ supersymmetric curvatures generalizing scalar curvature, Ricci curvature and Weyl tensor. These supercurvatures are the building blocks of various linearized $4D,\mathcal{N}=2$ Einstein supergravity invariants. The supercurvatures involving the scalar and Ricci curvatures are analytic harmonic $\mathcal{N}=2$ superfields, while the Weyl supertensor is a chiral $\mathcal{N}=2$ superfield. As the basic distinguished feature of our construction, all these objects are expressed through the fundamental analytic gauge prepotentials $h^{++M},M=(\hat{I}\pm \dot{\hat{I}}\pm ,+\hat{I}\pm ,+\dot{\hat{I}}\pm ,5)$. 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.

0 + 36 pages, slight corrections in signs, with no impact on the final results