Covariant superspace approaches to ${\cal N}=2$ supergravity

TL;DR

This paper unifies three covariant superspace formulations of ${ m N}=2$ supergravity in four dimensions, highlighting their structures, applications, and related invariants, to advance understanding of supergravity-matter systems.

Contribution

It provides a comprehensive comparison and description of the three covariant superspace approaches to ${ m N}=2$ supergravity, emphasizing their structures and applications.

Findings

Unified description of three superspace approaches

Application to supergravity-matter systems and sigma models

Discussion of higher-derivative and topological invariants

Abstract

We provide a unified description of the three covariant superspace approaches to ${\cal N}=2$ conformal supergravity in four dimensions: (i) conformal superspace; (ii) $\mathsf{U}(2)$ superspace; and (iii) $\mathsf{SU}(2)$ superspace. Each of them can be used to formulate general supergravity-matter systems, although conformal superspace has the largest structure group and is intimately related to the superconformal tensor calculus. We review the structure of covariant projective multiplets and demonstrate how they are used to describe pure and matter-coupled supergravity, including locally superconformal off-shell sigma models. Higher-derivative invariants, topological invariants and super-Weyl anomalies are also briefly discussed.