Instantons near a tachyonic top in anti de Sitter and the no-boundary regulator

摘要

We investigate instantons near a tachyonic top in an anti de Sitter (AdS)background. If the mass scale around the hill-top is above theBreitenlohner-Freedman (BF) bound, then the top is classically stable. When theBF bound is satisfied, it is already known that there can exist instantons witha non-zero probability, though fine-tunings of the potential are required. Onthe other hand, we may consider a possibility to obtain instantons with anon-zero probability for more natural shape of potentials. We found that theno-boundary regulator is useful to assign a non-zero probability for generalinstantons near the tachyonic top with a consistent framework. To use theno-boundary regulator, we need to introduce the complexification of fields. Oneinteresting feature is that, for these AdS instantons, the classicality may notbe satisfied after the Wick rotation and hence after the nucleation. Thismagnifies a novel difference between dS and AdS; a semi-classical boundaryobserver in AdS may notice the dispersion of quantum fields as a kind ofuncertainty, while every semi-classical observers in dS are classicalizedindividually and hence there is no semi-classical observer who can see thequantum dispersion of the scalar field.