Noether-Wald charge in supergravity: the fermionic contribution

Abstract

Abstract We study the invariance of $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 1, d = 4 supergravity with fermionic contributions which is diff- Lorentz- and supersymmetry-invariant (up to a total derivative).