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 ∆ 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 × S3.
Highlights
Systems with multiple ground states are common in many areas of physics
When is anti-de Sitter (AdS) vacuum decay possible? A question we address is under what circumstances O(D)-instanton solutions mediating AdS decay exist in a potential
It is hard to single out exactly which local features of a potential allow for instanton solutions, we are able to connect the existence of Coleman-de Luccia (CdL) instantons to another feature of the scalar potential: the existence of exotic holographic RG flows, [16]
Summary
Systems with multiple ground states are common in many areas of physics. The transitions from a higher energy ground state (false vacuum) to a lower energy one (true vacuum) can proceed via tunnelling, with the formation of a bubble which subsequently expands. The solutions (1.2) can be interpreted as holographic RG flows of QFTs defined on a d-dimensional space-time of constant positive curvature, with the UV fixed point corresponding to the false vacuum theory. In this case, as we shall review below, the flow cannot reach the true vacuum (i.e. the lower AdS minimum) but at the endpoint ξ → 0, it stops at a field value φ0 where V (φ0) = 0, [13]. We shall analyse these questions in general, and with the help of numerical analyses in a few explicit (but generic) examples
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