Supergravity at the boundary of AdS supergravity

TL;DR

This paper analyzes boundary conditions for Rarita-Schwinger fields in AdS spaces, identifying those that preserve supersymmetry, and explores their implications for AdS/CFT correspondence and boundary supergravity theories.

Contribution

It provides a comprehensive classification of supersymmetry-preserving boundary conditions for spin-3/2 fields in AdS, including mixed conditions for various masses, and applies these to N=1 AdS_4 supergravity.

Findings

Mixed boundary conditions are allowed for certain mass ranges.

Supersymmetric boundary conditions correspond to gauging superconformal groups.

Neumann boundary conditions relate to gauging superconformal symmetry in dual CFT.

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.