Revisiting Coleman-de Luccia transitions in the AdS regime using holography

TL;DR

This paper explores Coleman-de Luccia tunnelling in AdS spaces through holography, revealing how exotic RG flows relate to instanton solutions and their implications for dual quantum field theories.

Contribution

It establishes a connection between tunnelling solutions and exotic RG flows, constructing explicit potentials with instantons and analyzing their holographic duals.

Findings

Existence of instantons tied to exotic RG flows that skip or reverse fixed points.

Thin-walled instantons correspond to large operator dimensions in dual theories.

Instantons do not necessarily indicate instability in the dual QFT on flat space.

Abstract

Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possible fixed points or reverses direction in the coupling. This connection is employed to construct explicit potentials that admit Coleman-de Luccia instantons in AdS and to study the associated tunnelling solutions. Thin-walled instantons are observed to correspond to dual field theories with a parametrically large value of the dimension $\Delta$ for the operator dual to the scalar field, casting doubt on the attainability of this regime in holography. From the boundary perspective, maximally symmetric instantons describe the probability of symmetry breaking of the dual QFT in de Sitter. It is argued that, even when such instantons exist, they do not imply an instability of the same theory on flat space or on $R\times S^3$.