Examining Instabilities Due to Driven Scalars in AdS

TL;DR

This paper investigates how time-dependent boundary sources influence the stability and energy dynamics of scalar fields in Anti-de Sitter space, revealing new insights into driven perturbations and their effects on turbulence.

Contribution

It extends the non-linear perturbative framework of AdS turbulence to include driven systems with time-dependent boundary sources, deriving analytic secular term expressions.

Findings

Derived analytic secular terms for driven scalar fields in AdS.

Numerically evaluated driven sources in 4D AdS.

Discussed implications for perturbative stability of AdS.

Abstract

We extend the study of the non-linear perturbative theory of weakly turbulent energy cascades in AdS$_{d+1}$ to include solutions of driven systems, i.e. those with time-dependent sources on the AdS boundary. This necessitates the activation of non-normalizable modes in the linear solution for the massive bulk scalar field, which couple to the metric and normalizable scalar modes. We determine analytic expressions for secular terms in the renormalization flow equations for any mass, and for various driving functions. Finally, we numerically evaluate these sources for $d = 4$ and discuss what role these driven solutions play in the perturbative stability of AdS.