Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry

Abstract

We use a covariant phase space formalism to give a general prescription for defining Hamiltonian generators of bosonic and fermionic symmetries in diffeomorphism invariant theories, such as supergravities. A simple and general criterion is derived for a choice of boundary condition to lead to conserved generators of the symmetries on the phase space. In particular, this provides a criterion for the preservation of supersymmetries. For bosonic symmetries corresponding to diffeomorphisms, our prescription coincides with the method of Wald et al. We then illustrate these methods in the case of certain supergravity theories in $d=4$. In minimal AdS supergravity, the boundary conditions such that the supercharges exist as Hamiltonian generators of supersymmetry transformations are unique within the usual framework in which the boundary metric is fixed. In extended $\mathcal{N}=4$ AdS supergravity, or more generally in the presence of chiral matter superfields, we find that there exist many boundary conditions preserving $\mathcal{N}=1$ supersymmetry for which corresponding generators exist. These choices are shown to correspond to a choice of certain arbitrary boundary ``superpotentials,'' for suitably defined ``boundary superfields.'' We also derive corresponding formulae for the conserved bosonic charges, such as energy, in those theories, and we argue that energy is always positive, for any supersymmetry-preserving boundary conditions. We finally comment on the relevance and interpretation of our results within the AdS-CFT correspondence.

arXiv comment45 pages, Latex, no figures, v2: extended discussion of positive energy theorem and explicit form of fermionic generators, references added

References in corpus (20)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Lecture Notes on Holographic Renormalization
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• "Double-trace" Deformations, Boundary Conditions and Spacetime Singularities
• Comparison between various notions of conserved charges in asymptotically AdS-spacetimes
• Holography of the N=1 Higher-Spin Theory on AdS4
• Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity
• SL(2,Z) Action on Three-Dimensional CFTs and Holography
• A Note on Multi-trace Deformations and AdS/CFT
• Energy Bounds in Designer Gravity
• Stability in Designer Gravity
• Consistent boundary conditions for supergravity
• A Note on AdS/CFT Dual of SL(2,Z) Action on 3D Conformal Field Theories with U(1) Symmetry
• The Wess-Zumino Model and the AdS_4/CFT_3 Correspondence

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