AdS/CFT beyond the unitarity bound

TL;DR

This paper investigates boundary conditions for scalar fields in AdS beyond the unitarity bound, showing that certain conformally-invariant boundary conditions remain ghost-free due to gauge modes and infrared effects, challenging previous assumptions.

Contribution

It demonstrates that boundary conditions beyond the unitarity bound can be ghost-free in AdS, revealing new insights into the AdS/CFT correspondence and boundary condition effects.

Findings

Conformally-invariant boundary conditions can be ghost-free beyond the unitarity bound.

Infrared divergences and gauge modes prevent ghosts in certain boundary conditions.

Removing IR divergences introduces ghosts, aligning with unitarity expectations.

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 Poincar\'e 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.