Noether-Wald charge in supergravity: the fermionic contribution

TL;DR

This paper derives a supersymmetry-invariant Noether-Wald charge in N=1, d=4 supergravity, incorporating fermionic contributions and clarifying the role of superpartner transformations in preserving invariance.

Contribution

It introduces a method to construct a diff-, Lorentz-, and supersymmetry-invariant Noether-Wald charge in supergravity, including fermionic effects, extending previous purely bosonic formulations.

Findings

Constructed a fermionic-inclusive Noether-Wald charge for supergravity.

Demonstrated invariance of the charge under local supersymmetry transformations.

Linked supersymmetry transformations to diffeomorphism invariance in supergravity.

Abstract

We study the invariance of N=1,d=4 supergravity solutions under diffeormophisms and show that, in order to obtain consistent conditions (``Killing equations'') invariant under local supersymmetry transformations, one has to perform supersymmetry transformations generated by the superpartner of the vector that generates standard diffeomorphisms, just as a superspace analysis indicates. Using these transformations, we construct a Noether-Wald charge of N=1,d=4 supergravity with fermionic contributions which is diff- Lorentz- and supersymmetry-invariant (up to a total derivative).