Massive symmetric tensor field on AdS

TL;DR

This work computes the two-point function of the CFT operator dual to a massive symmetric tensor field on $AdS_{d+1}$ via the AdS/CFT correspondence. By solving the coupled bulk equations of motion for $\phi_{\mu\nu}$ with mass, using $x_0=\varepsilon$ regularization, and isolating the boundary nonlocal contribution to the on-shell action, the authors derive an explicit boundary two-point function with a transverse-traceless tensor structure. In the massless limit ($Δ\to d/2$) the result reduces to the known graviton two-point function, providing a consistency check and filling a gap in the holographic mapping for massive higher-rank fields. The normalization $C_{d,Δ}$ and the tensor projector built from $J^i_j$ give a precise prediction for the boundary correlator, strengthening the link between bulk massive tensors and CFT operators.

Abstract

The two-point Green function of a local operator in CFT corresponding to a massive symmetric tensor field on the AdS background is computed in the framework of the AdS/CFT correspondence. The obtained two-point function is shown to coincide with the two-point function of the graviton in the limit when the mass vanishes.