Supergravity at the boundary of AdS supergravity

TL;DR

This work analyzes AdS boundary conditions for spin-3/2 RS fields and classifies supersymmetric boundary conditions for the graviton multiplet in AdS$_4$. It develops a holographic renormalization framework with a renormalized symplectic structure to realize mixed and Neumann boundary conditions beyond the standard range, and applies it to ${\cal N}=1$ AdS$_4$ supergravity to identify boundary stress tensors, supercurrents, and SUSY-preserving boundary data. The main results show mixed Dirichlet–Neumann BCs for $0\le |m| < 1/(2 l_{AdS})$, with Neumann-type and mixed BCs extending to larger masses after renormalization; in d=4 this yields a boundary 3D conformal supergravity and connections to supersymmetric topologically massive gravity. The findings illuminate how dynamical boundary gravity and boundary SUSY emerge in AdS/CFT, offering a path to study deformations and unitarity constraints in holographic setups with fluctuating boundary geometry.

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 AdS_4. Linear Rarita-Schwinger fields in AdS_d are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range $0 \leq |m| < 1/2l_{AdS}$. 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_{AdS} to explore supersymmetric boundary conditions for N = 1 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 3-dimensional CFT describing M2-branes, while N = 1 supersymmetric mixed boundary conditions couple the CFT to N = 1 superconformal topologically massive gravity.