Isometries of N=1 4D supergravity

TL;DR

This paper generalizes the concept of isometries in supergravity by deriving a superfield-based extension of Killing equations that includes the entire supergravity multiplet, accommodating non-zero Rarita-Schwinger fields.

Contribution

It introduces a superfield approach to extend Killing equations in supergravity, allowing for non-vanishing Rarita-Schwinger fields in isotropic spacetimes.

Findings

Derived a superfield-based generalization of Killing equations.

Allowed for non-zero Rarita-Schwinger fields in isotropic supergravity solutions.

Provided a framework consistent with supergravity principles.

Abstract

Continuous symmetries of spacetime such as spatial homogeneity and isotropy are rigorously defined using the concept of isometries and Killing vectors. In supergravity, the metric, or rather the tetrad, is not a standalone entity, but is part of a multiplet containing also the Rarita-Schwinger spinor-vector. Thus, we pursue a generalization of the Killing equations that is in harmony with the tenets of supergravity. Using a superfield approach, we derive one such generalization of the Killing equations encompassing the whole supergravity multiplet. A relaxation of the spinor-vector equations is required to allow for a non-vanishing isotropic Rarita-Schwinger field.