# New islands of stability with double-trace deformations

## TL;DR

This paper investigates how altering boundary conditions in Anti-de Sitter space affects the stability of solutions, revealing that non-resonant conditions can stabilize multi-oscillator solutions, unlike fully resonant cases.

## Contribution

It demonstrates that breaking the resonant spectrum with specific boundary conditions can create stable, non-collapsing solutions in AdS, challenging previous assumptions about resonance and stability.

## Key findings

- Non-collapsing two-mode solutions exist in non-resonant Robin boundary conditions.
- Such solutions disappear in the fully resonant Dirichlet case.
- Neumann boundary conditions allow near-AdS solutions that are not single-mode dominated.

## Abstract

We assess the role of a resonant spectrum in the AdS instability, and quantify the extent to which breaking the resonant spectrum of AdS can restore stability. Specifically, we study non-collapsing `multi-oscillator' solutions in AdS under various boundary conditions that allow for both resonant and non-resonant spectra. We find non-collapsing two mode, equal amplitude solutions in the non-resonant Robin case, and that these solutions vanish in the fully resonant Dirichlet case. This is consistent with non-resonant stability, and with the idea that stable solutions in the Dirichlet case are all single-mode dominated. Surprisingly, when the boundary condition is Neumann, we find non-collapsing solutions arbitrarily close to AdS that are not single-mode dominated, despite the spectrum being fully resonant.