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

TL;DR

This paper constructs linearized off-shell superinvariants in 4D, N=2 supergravity using harmonic superspace, introducing supercurvatures as fundamental building blocks expressed via gauge prepotentials.

Contribution

It introduces a harmonic superspace framework for off-shell invariants in 4D, N=2 supergravity, generalizing curvature superfields and expressing them through gauge prepotentials.

Findings

Supercurvatures generalize scalar, Ricci, and Weyl tensors.

Supercurvatures are expressed as analytic or chiral superfields.

Component reduction examples illustrate the invariants.

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 ${\cal N}=2$ 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 $h^{++M}, M= (\alpha\dot\alpha, +\alpha, +\dot\alpha, 5)$. 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.