A note on causality in the bulk and stability on the boundary

TL;DR

This paper investigates how the stability of boundary perturbations in a holographic setup can be detected through the bulk scalar field spectrum, revealing a bound state indicating instability via AdS/CFT correspondence.

Contribution

It demonstrates that the bulk scalar field spectrum encodes boundary stability information, linking bound states to unstable boundary deformations in holography.

Findings

Bound states in the bulk spectrum indicate boundary instability.

Certain boundary conditions lead to a bound state in the radial spectrum.

Bulk analysis detects boundary perturbation stability via spectral features.

Abstract

By carefully analyzing the radial part of the wave-equation for a scalar field in AdS, we show that for a particular range of boundary conditions on the scalar field, the radial spectrum contains a bound state. Using the AdS/CFT correspondence, we interpret this peculiar phenomenon as being dual to an unstable double trace deformation of the boundary conformal field theory. We thus show how the bulk theory holographically detects whether a boundary perturbation is stable.