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

TL;DR

This paper explores instantons near a tachyonic top in anti de Sitter space, demonstrating the usefulness of the no-boundary regulator and revealing differences in classicality post-nucleation between AdS and dS spaces.

Contribution

It introduces a framework using the no-boundary regulator with complexified fields to assign probabilities to instantons near a tachyonic top in AdS, highlighting differences from de Sitter space.

Findings

The no-boundary regulator enables assigning non-zero probabilities to instantons in AdS.

Classicality may not be preserved after nucleation in AdS instantons.

Quantum dispersion effects are observable in AdS but not in dS for semi-classical observers.

Abstract

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.