Supergravity at the boundary of AdS supergravity

Abstract

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 ${\mathrm{AdS}}_{4}$. Linear Rarita-Schwinger fields in ${\mathrm{AdS}}_{d}$ are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range $0\ensuremath{\le}|m|<1/2{l}_{\mathrm{AdS}}$. 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 $|m|=1/{l}_{\mathrm{AdS}}$ to explore supersymmetric boundary conditions for $\mathcal{N}=1$ ${\mathrm{AdS}}_{4}$ 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 $\mathcal{N}=1$ supersymmetric mixed boundary conditions couple the CFT to $\mathcal{N}=1$ superconformal topologically massive gravity.