  We investigate instantons near a tachyonic top in an anti de Sitter (AdS)
background. If the mass scale around the hill-top is above the
Breitenlohner-Freedman (BF) bound, then the top is classically stable. When the
BF bound is satisfied, it is already known that there can exist instantons with
a non-zero probability, though fine-tunings of the potential are required. On
the other hand, we may consider a possibility to obtain instantons with a
non-zero probability for more natural shape of potentials. We found that the
no-boundary regulator is useful to assign a non-zero probability for general
instantons near the tachyonic top with a consistent framework. To use the
no-boundary regulator, we need to introduce the complexification of fields. One
interesting feature is that, for these AdS instantons, the classicality may not
be satisfied after the Wick rotation and hence after the nucleation. This
magnifies a novel difference between dS and AdS; a semi-classical boundary
observer in AdS may notice the dispersion of quantum fields as a kind of
uncertainty, while every semi-classical observers in dS are classicalized
individually and hence there is no semi-classical observer who can see the
quantum dispersion of the scalar field.
