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We use a covariant phase space formalism to give a general prescription fordefining Hamiltonian generators of bosonic and fermionic symmetries indiffeomorphism invariant theories, such as supergravities. A simple and generalcriterion is derived for a choice of boundary condition to lead to conservedgenerators of the symmetries on the phase space. In particular, this provides acriterion for the preservation of supersymmetries. For bosonic symmetriescorresponding to diffeomorphisms, our prescription coincides with the method ofWald et al.  We then illustrate these methods in the case of certain supergravity theoriesin $d=4$. In minimal AdS supergravity, the boundary conditions such that thesupercharges exist as Hamiltonian generators of supersymmetry transformationsare unique within the usual framework in which the boundary metric is fixed. Inextended ${\mathcal N}=4$ AdS supergravity, or more generally in the presenceof chiral matter superfields, we find that there exist many boundary conditionspreserving ${\mathcal N}=1$ supersymmetry for which corresponding generatorsexist. These choices are shown to correspond to a choice of certain arbitraryboundary ``superpotentials,'' for suitably defined ``boundary superfields.'' Wealso derive corresponding formulae for the conserved bosonic charges, such asenergy, in those theories, and we argue that energy is always positive, for anysupersymmetry-preserving boundary conditions. We finally comment on therelevance and interpretation of our results within the AdS-CFT correspondence.Comment: 45 pages, Latex, no figures, v2: extended discussion of positive  energy theorem and explicit form of fermionic generators, references adde

Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry