AdS Vacuum Bubbles, Holography and Dual RG Flows

TL;DR

This paper investigates how non-perturbative vacuum decay in AdS geometries relates to boundary RG flows, using holographic entanglement entropy to understand the dual field theory dynamics and the structure of holographic RG flows.

Contribution

It establishes a connection between vacuum bubble nucleation in AdS and relevant deformations inducing RG flows in the dual theory, utilizing holographic entanglement entropy as a $c$-function.

Findings

Vacuum decay corresponds to relevant boundary deformations.

Entanglement entropy acts as a $c$-function along RG flows.

Holographic integral geometry provides insights into RG flow structure.

Abstract

We explore the holographic properties of non-perturbative vacuum decay in Anti-de Sitter ($\mathrm{AdS}$) geometries. To this end, we consider a gravitational theory in a metastable $\mathrm{AdS}_3$ state, which decays into an $\mathrm{AdS}_3$ of lower vacuum energy via bubble nucleation, and we employ the Ryu-Takayanagi conjecture to compute the entanglement entropy $S_\text{ent}$ in its alleged holographic dual. Our analysis leads us to infer that the nucleation and growth of a vacuum bubble correspond, in the boundary theory, to the introduction of a relevant deformation and a subsequent Renormalization Group (RG) flow, where $S_\text{ent}$ provides a $c$-function. We provide further evidence for the claim and comment on the holographic interpretation of off-centred or multiple bubbles. We also frame the issue in the formalism of Holographic Integral Geometry, discussing the consequences on the structure of the holographic RG flow and recovering the standard holographic RG as a limiting case.