Is the Coleman de Luccia action minimum?: AdS/CFT approach

TL;DR

This paper uses AdS/CFT duality to demonstrate that the Coleman de Luccia bounce action is minimal in AdS spaces under specific conditions, resolving issues related to gravitational metastable decay.

Contribution

It establishes the minimality of the Coleman de Luccia bounce action in AdS using the dual CFT perspective, addressing challenges of negative modes and unbounded actions.

Findings

Fubini bounce in CFT corresponds to minimal bounce in AdS.

Coleman de Luccia action is minimal when AdS radii are nearly equal.

Results apply to thin-wall bounces in metastable AdS vacua.

Abstract

We use the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to find the least bounce action in an AdS false vacuum state, i.e., the most probable decay process of the metastable AdS vacuum within the Euclidean formalism by Callan and Coleman. It was shown that the $O(4)$ symmetric bounce solution leads to the action minimum in the absence of gravity, but it is non-trivial in the presence of gravity. The AdS/CFT duality is used to evade the difficulties particular to a metastable gravitational system, such as the problems of negative modes and unbounded action. To this end, we show that the Fubini bounce solution in CFT, corresponding to the Coleman de Luccia bounce in AdS, gives the least action among all finite bounce solutions in a conformal scalar field theory. Thus, we prove that the Coleman de Luccia action is the least action when (i) the background is AdS, (ii) the AdS radii, $L_+$ and $L_-$, in the false and true vacua, respectively, satisfy $L_+ / L_- \simeq 1$, and (iii) a metastable potential gives a thin-wall bounce much larger than the AdS radii.