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.Comment: 20 pages, 9 figure