\(\mathcal{N} = 2\) Supergravity and Harmonic Superspace: Linearized Supercurvatures

Abstract

Using the formulation of \(\mathcal{N} = 2\) supergravity in harmonic superspace, we construct a complete set of linearized supercurvatures that are \(\mathcal{N} = 2\) supersymmetrizations of the scalar curvature, the irreducible part of the Ricci tensor and the self-dual Weyl tensor. Based on these supercurvatures, the total set of quadratic invariants of the linearized \(\mathcal{N} = 2\) supergravity is constructed. Supercurvaturies have a beautiful geometric structure and admit a generalization to higher spins, thereby opening the way towards the construction of a number of \(\mathcal{N} = 2\) supersymmetric cubic interactions of such spins.