Off-shell invariants of linearized 4 D , N = 2 supergravity in the harmonic approach

Source abstract

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 4 D , 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 = ( α α ˙ , α + , α ˙ + , 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. Published by the American Physical Society 2024