Supergravity at the boundary of AdS supergravity

We give a general analysis of AdS boundary conditions for spin-3/2 Rarita-Schwinger fields and investigate boundary conditions preserving supersymmetry for a graviton multiplet in AdS4. Linear Rarita-Schwinger fields in AdSd are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range 0≤|m|<1/2lAdS. We also demonstrate that mixed boundary conditions are allowed for larger masses when the inner product is 'renormalized' accordingly with the action. We then use the results obtained for |m|=1/lAdS to explore supersymmetric boundary conditions for N=1 AdS4 supergravity in which the metric and Rarita-Schwinger fields are fluctuating at the boundary. We classify boundary conditions that preserve boundary supersymmetry or superconformal symmetry. Under the AdS/CFT dictionary, Neumann boundary conditions in d=4 supergravity correspond to gauging the superconformal group of the three-dimensional CFT describing M2-branes, while N=1 supersymmetric mixed boundary conditions couple the CFT to N=1 superconformal topologically massive gravity.