Noether-Wald and Komar charges in supergravity, fermions, and Killing supervectors in superspace

TL;DR

This paper explores the relationship between Killing vectors, spinors, and supervectors in supergravity, constructing invariant charges and analyzing superspace formulations to clarify supersymmetry properties.

Contribution

It introduces a Noether-Wald charge in supergravity that includes fermionic contributions and discusses Killing supervectors in superspace and maximal supergravity.

Findings

Constructed a supersymmetry-invariant Noether-Wald charge for ${ m N}=1$, $D=4$ supergravity.

Clarified the relation between Killing vectors, spinors, and supervectors in superspace.

Discussed Killing supervector formalism in maximal $D=11$ supergravity.

Abstract

The supersymmetry properties of Killing vectors and spinors in supergravity theory can be clarified by relating them to Killing supervectors in the supergravity superspace. In the superspace approach it is manifest that supersymmetry 'mixes' a Killing vector with its fermionic spinor 'superpartner' and the Killing equations with the generalization of the Killing spinor equations. The latter reduces to the standard Killing spinor equation, albeit with a fermionic spinor, when the fermionic fields are set to zero. Using these supersymmetry transformations in the spacetime component approach, we construct a Noether-Wald charge of ${\cal N}=1$, $D=4$ supergravity with fermionic contributions which is diff-, Lorentz- and supersymmetry-invariant (up to a total derivative). The Killing supervector formalism for the maximal $D=11$ supergravity and some related issues are also discussed.