AdS/CFT beyond the unitarity bound

TL;DR

This work analyzes AdS/CFT with bulk scalars in the Breitenlohner-Freedman window and beyond, focusing on non-Dirichlet boundary conditions. By formulating a renormalized Klein-Gordon inner product and performing a Sturm–Liouville analysis in the Poincaré patch, it finds that conformally invariant Neumann boundary conditions can be ghost-free due to infrared divergences and pure gauge modes, even when ν ≥ 1. Ghosts reappear if the IR divergence is regulated, either by boundary deformations or in global AdS, illustrating a subtle interplay between unitarity bounds and infrared structure in holographic duals. The results bridge scalar, Maxwell, and gravitational cases, highlighting how boundary terms and gauge content shape the physical spectrum and dual operator dimensions in AdS/CFT.

Abstract

Scalars in AdS${}_{d+1}$ with squared masses in the Breitenlohner-Freedman window $-d^2/4 \le m^2 < -d^2/4 +1$ (in units with the AdS scale $\ell$ set to 1) are known to enjoy a variety of boundary conditions. For larger masses $m^2 > -d^2/4 +1$, unitarity bounds in possible dual CFTs suggest that such general boundary conditions should lead to ghosts. We show that this is not always the case as, for conformally-invariant boundary conditions in Poincaré AdS that would naively violate unitarity bounds, the system is generically ghost-free. Conflicts with unitarity bounds are avoided due to the presence of unexpected pure gauge modes and an associated infrared divergence. The expected ghosts appear when the IR divergence is removed either by deforming these boundary conditions or considering global AdS.