Supergravities in Four Dimensions

Abstract

Supergravity is a field theory of gravity which has local supersymmetry. It contains a gravitational field and Rarita–Schwinger fields besides other types of fields. We first discuss supermultiplets of the $\fancyscript{N}=1$ super Poincaré algebra and globally supersymmetric field theories in four-dimensional Minkowski spacetime. We then consider $\fancyscript{N}=1$ Poincaré supergravity and give the Lagrangian and the local symmetry transformation laws. We also discuss anti de Sitter supergravity, which has a cosmological term and a mass term of the Rarita–Schwinger field. Next, we consider supergravities with extended supersymmetry. The Lagrangians and the local symmetry transformation laws are explicitly given for $\fancyscript{N}=2$ Poincaré and anti de Sitter supergravities. Finally, we discuss the general structure of $\fancyscript{N} \ge 3$ extended supergravities briefly.