Living with ghosts in Lorentz invariant theories
  We argue that theories with ghosts may have a long lived vacuum state even if
all interactions are Lorentz preserving. In space-time dimension D = 2, we
consider the tree level decay rate of the vacuum into ghosts and ordinary
particles mediated by non-derivative interactions, showing that this is finite
and logarithmically growing in time. For D > 2, the decay rate is divergent
unless we assume that the interaction between ordinary matter and the ghost
sector is soft in the UV, so that it can be described in terms of non-local
form factors rather than point-like vertices. We provide an example of a
nonlocal gravitational-strength interaction between the two sectors, which
appears to satisfy all observational constraints.
