${\cal N}=2\,$ Supergravities in Harmonic Superspace

TL;DR

This paper reviews the formulation of ${ m N}=2$, 4D supergravities in harmonic superspace, highlighting the off-shell supermultiplets, geometric interpretation, and construction of superfield actions for various supergravity models.

Contribution

It introduces a harmonic superspace approach to ${ m N}=2$, 4D supergravities, providing off-shell formulations with geometric meaning and explicit superfield actions.

Findings

Off-shell supermultiplets are represented by harmonic-analytic prepotentials.

Superfield actions for ${ m N}=2$ Einstein supergravity are constructed.

The principal version allows general couplings to quaternion-K"ahler matter.

Abstract

Basics of ${\cal N}=2, 4D$ conformal and Einstein supergravities in the harmonic superspace approach are outlined. The crucial merit of this formulation consists in that the relevant off-shell supermultiplets, in particular ${\cal N}=2, 4D$ superconformal Weyl multiplet, are accommodated by the harmonic-analytic unconstrained prepotentials with a clear geometric meaning, like in the analogous formulation of ${\cal N}=2, 4D$ supersymmetric gauge theory. The fundamental gauge group of conformal supergravity is constituted by the analyticity-preserving diffeomorphisms of harmonic superspace. The superfield actions of various off-shell versions of ${\cal N}=2$ Einstein supergravity are obtained as the actions of the appropriate harmonic analytic compensators in the background of conformal ${\cal N}=2$ supergravity. The version admitting the most general couplings to quaternion-K\"ahler matter is the ``principal'' version with the unconstrained harmonic analytic hypermultiplet superfield as a compensator. It involves an infinite number of auxiliary fields.