Linearized N = 2 conformal supergravity in the harmonic approach

A bstract Using the harmonic superspace approach, we construct the superconformal harmonic action for N N = 2 Weyl supermultiplet. The fundamental objects of the theory are unconstrained analytic potentials h++α α̇ h + + α α ̇ , h ++ α + , h++α̇+ 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 N N = 2 Weyl action to large extent repeats the structure of the N N = 2 Maxwell action, which suggests a conjecture on the possible structure of the complete nonlinear 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 N N = 2 Weyl action, based on an analogy with N N = 2 Maxwell action just mentioned and a generalization of the concept of half-analyticity to curved harmonic superspace.