Coupled boundary and bulk fields in anti-de Sitter

TL;DR

This paper studies the interaction between boundary and bulk fields in anti-de Sitter space, revealing conditions for stability, bound states, and instabilities, with implications for brane-world models and gravitational perturbations.

Contribution

It introduces an instability criterion for coupled boundary and bulk fields in AdS, identifying conditions for tachyonic bound states and stable quasi-normal modes.

Findings

Tachyonic bound states occur above a critical coupling.

Stable oscillations with finite decay times are observed below the critical coupling.

A massless stable bound state exists only at the critical coupling.

Abstract

We investigate the dynamics of a boundary field coupled to a bulk field with a linear coupling in an anti-de Sitter bulk spacetime bounded by a Minkowski (Randall-Sundrum) brane. An instability criterion for the coupled boundary and bulk system is found. There exists a tachyonic bound state when the coupling is above a critical value, determined by the masses of the brane and bulk fields and AdS curvature scale. This bound state is normalizable and localised near the brane, and leads to a tachonic instability of the system on large scales. Below the critical coupling, there is no tachyonic state and no bound state. Instead, we find quasi-normal modes which describe stable oscillations, but with a finite decay time. Only if the coupling is tuned to the critical value does there exist a massless stable bound state, as in the case of zero coupling for massless fields. We discuss the relation to gravitational perturbations in the Randall-Sundrum brane-world.