Rarita-Schwinger Field in the AdS/CFT Correspondence

TL;DR

This work extends the AdS/CFT dictionary to the Rarita–Schwinger field by showing that a boundary term supplements the bulk action and acts as the generating functional for spin-3/2 boundary correlators. It solves the RS equations on Euclidean AdS_{d+1}, identifies the boundary data, and derives the finite boundary action whose form reproduces the CFT two-point function fixed by conformal invariance, establishing Δ = d/2 + m. The explicit boundary term and mass–dimension relation are demonstrated and connected to known spectra, e.g., m = 3/2 in IIB supergravity on AdS_5 × S^5 yielding Δ = 7/2 for the supersymmetry current. Collectively, the results validate generating-function approaches for fermionic higher-spin fields in AdS/CFT and link bulk masses to boundary operator dimensions.

Abstract

A free Rarita-Schwinger field in the Anti-de Sitter space is considered. We show that the usual action can be supplemented by a boundary term that can be interpreted as the generating functional of the correlation functions in a conformal field theory on the boundary of the Anti-de Sitter space.