The missing top of AdS resonance structure

Abstract

We study a massless scalar field in AdS_{d+1} with a nonlinear coupling ϕ^N and not limited to spherical symmetry. The free-field-eigenstate spectrum is strongly resonant, and it is commonly believed that the nonlinear coupling leads to energy transfer between eigenstates. We prove that when $Nd$ is even, the most efficient resonant channels to transfer energy are always absent. In particular, for N=3 this means no energy transfer at all. For N=4, this effectively kills half of the channels, leading to the same set of extra conservation laws recently derived for gravitational interactions within spherical symmetry.

arXiv comment12 pages, no figures, version 2 that mutes "showkeys" correctly and added one reference

References in corpus (17)

• Holographic representation of local bulk operators
• On weakly turbulent instability of anti-de Sitter space
• Oscillons: Resonant Configurations During Bubble Collapse
• Pseudo-Stable Bubbles
• Local bulk operators in AdS/CFT: A holographic description of the black hole interior
• Holographic Thermalization, stability of AdS, and the Fermi-Pasta-Ulam-Tsingou paradox
• On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions
• Gravitational Turbulent Instability of Anti-de Sitter Space
• Renormalization group, secular term resummation and AdS (in)stability
• Time-periodic solutions in Einstein AdS - massless scalar field system
• Renormalization, averaging, conservation laws and AdS (in)stability
• Globally regular instability of $Ad{S}_3$
• K-Oscillons: Oscillons with Non-Canonical Kinetic Terms
• Conserved quantities and dual turbulent cascades in Anti-de Sitter spacetime
• What drives AdS unstable?
• Position space analysis of the AdS (in)stability problem
• A Stochasticity Threshold in Holography and and the Instability of AdS

Cited by in corpus (30)

• Numerical Methods for Finding Stationary Gravitational Solutions
• Islands of stability and recurrence times in AdS
• A Hidden Symmetry of AdS Resonances
• AdS perturbations, isometries, selection rules and the Higgs oscillator
• Ultraviolet asymptotics and singular dynamics of AdS perturbations
• Collapse and Nonlinear Instability of AdS with Angular Momenta
• AdS (In)stability: Lessons From The Scalar Field
• AdS (in)stability: an analytic approach
• Conformal flow on $S^3$ and weak field integrability in AdS${}_4$
• Self-gravitating scalar breathers with negative cosmological constant
• Conditionally Extended Validity of Perturbation Theory: Persistence of AdS Stability Islands
• Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
• AdS nonlinear instability: moving beyond spherical symmetry
• Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes
• Maximally rotating waves in AdS and on spheres
• Moving Closer to the Collapse of a Massless Scalar Field in Spherically Symmetric Anti-de Sitter Spacetimes
• Klein-Gordonization: mapping superintegrable quantum mechanics to resonant spacetimes
• Necessary conditions for an AdS-type instability
• Charting the AdS Islands of Stability with Multi-oscillators?
• Complex plane representations and stationary states in cubic and quintic resonant systems
• Coherent Cascade Conjecture for Collapsing Solutions in Global AdS
• AdS nonlinear instability: breaking spherical and axial symmetries
• Energy returns in global AdS_4
• Fully resonant scalars on asymptotically AdS wormholes
• Hidden symmetries of the Higgs oscillator and the conformal algebra
• - Gravitational Waves - A Review on the Conceptual Foundations of Gravitational Radiation
• Fast and Slow Coherent Cascades in Anti-de Sitter Spacetime
• Time-periodicities in holographic CFTs
• Spectroscopy instead of scattering: particle experimentation in AdS spacetime
• Gravitational systems in asymptotically anti-de Sitter space-times