Banishing AdS ghosts with a UV cutoff

A recent attempt to make sense of scalars in AdS with "Neumann boundary conditions" outside of the usual BF-window -(d/2)² < m²l² < -(d/2)² +1 led to pathologies including (depending on the precise context) either IR divergences or the appearance of ghosts. Here we argue that such ghosts may be banished by imposing a UV cutoff. It is also possible to achieve this goal in certain UV completions. An example is the above AdS theory with a radial cutoff supplemented by particular boundary conditions on the cutoff surface. In this case we explicitly identify a region of parameter space for which the theory is ghost free. At low energies, this theory may be interpreted as the standard dual CFT (defined with "Dirichlet" boundary conditions) interacting with an extra scalar via an irrelevant interaction. We also discuss the relationship to recent works on holographic fermi surfaces and quantum criticality.