The massless gravitino and the AdS/CFT correspondence

TL;DR

The paper addresses the AdS/CFT correspondence for the massless gravitino on Euclidean $AdS_{d+1}$ by solving the Dirichlet boundary-value problem and computing the two-point function of the dual CFT supersymmetry currents. The authors carefully regularize the on-shell action with a boundary term and exploit the first-order nature of the gravitino equations to show that boundary data effectively consists of a $(d-1)$-dimensional gravitino, akin to the spinor case. They derive the bulk solutions using momentum-space decomposition and Bessel functions, then extract the boundary two-point function, obtaining a structure proportional to a transverse projection operator and the $|\mathbf{y}_1-\mathbf{y}_2|^{-(d+\Lambda+1)}$ scaling with dimension $\eta=(d+\Lambda)/2$. The results align with CFT expectations for the supersymmetry current and set the stage for incorporating interactions and full Ward-identity checks in future work.

Abstract

We solve the Dirichlet boundary value problem for the massless gravitino on $AdS_{d+1}$ space and compute the two-point function of the dual CFT supersymmetry currents using the $AdS$/CFT correspondence principle. We find analogously to the spinor case that the boundary data for the massless $(d+1)$ dimensional bulk gravitino field consists of only a $(d-1)$ dimensional gravitino.