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

A

bstract

Using the harmonic superspace approach, we construct the superconformal harmonic action for

= 2 Weyl supermultiplet. The fundamental objects of the theory are unconstrained analytic potentials

$$ {h}^{++\alpha \dot{\alpha}} $$ h + + α α ̇

, h ^{++ α +} ,

$$ {h}^{++\dot{\alpha}+} $$ h + + α ̇ +

, 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. The structure of the harmonic linearized

$$ \mathcal{N} $$ N

= 2 Weyl action to large extent repeats the structure of the

$$ \mathcal{N} $$ N

= 2 Maxwell action, which suggests a conjecture on the possible structure of the complete nonlinear

$$ \mathcal{N} $$ N

= 2 Weyl theory action in the harmonic superspace. We provide a detailed study of the rigid superconformal properties of the proposed action and prove its invariance in both harmonic and chiral superspaces. First steps are also undertaken towards constructing the nonlinear

$$ \mathcal{N} $$ N

= 2 Weyl action, based on an analogy with

$$ \mathcal{N} $$ N

= 2 Maxwell action just mentioned and a generalization of the concept of half-analyticity to curved harmonic superspace.