Linearized $\mathcal{N}=2$ conformal supergravity in the harmonic approach

TL;DR

This paper constructs a superconformal harmonic action for $ abla=2$ Weyl supermultiplet using harmonic superspace, introducing unconstrained potentials and analyzing its properties and invariance, suggesting a structure for the full nonlinear theory.

Contribution

It introduces a novel harmonic superspace formulation for $ abla=2$ Weyl supermultiplet with unconstrained potentials, expanding the understanding of superconformal actions.

Findings

The harmonic linearized $ abla=2$ Weyl action resembles the $ abla=2$ Maxwell action.

The construction involves unconstrained analytic potentials $h^{++ullet}$.

The action is invariant under superconformal transformations in harmonic and chiral superspaces.

Abstract

Using the harmonic superspace approach we construct the superconformal harmonic action for $\mathcal{N}=2$ Weyl supermultiplet. The fundamental objects of the theory are unconstrained analytic potentials $h^{++\alpha\dot{\alpha}}, h^{++\alpha+}, h^{++\dot{\alpha}+}, h^{(+4)}$, which distinguishes our construction among the previously known ones. An important role is played by the ``half-analyticity'' conditions introduced in arxiv:2407.08524 [hep-th]. The structure of the harmonic linearized $\mathcal{N}=2$ Weyl action to large extent repeats the structure of the $\mathcal{N}=2$ Maxwell action, which suggests a conjecture on the possible structure of the complete nonlinear $\mathcal{N}=2$ Weyl theory action in the harmonic superspace. We also provide a detailed study of the rigid superconformal properties of the proposed action and prove its invariance in both harmonic and chiral superspaces.