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arXiv · 2407.08524

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

Evgeny Ivanov·Nikita Zaigraev
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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.

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Evgeny Ivanov, Nikita Zaigraev. 2024-07-11. Off-shell invariants of linearized $4D, \mathcal{N}=2$ supergravity in the harmonic approach. https://doi.org/10.1103/physrevd.110.066020

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