Renormalization group, secular term resummation and AdS (in)stability
arXiv:1407.6273 · doi:10.1007/JHEP10(2014)048
Abstract
We revisit the issues of non-linear AdS stability, its relation to growing (secular) terms in naive perturbation theory around the AdS background, and the need and possible strategies for resumming such terms. To this end, we review a powerful and elegant resummation method, which is mathematically identical to the standard renormalization group treatment of ultraviolet divergences in perturbative quantum field theory. We apply this method to non-linear gravitational perturbation theory in the AdS background at first non-trivial order and display the detailed structure of the emerging renormalization flow equations. We prove, in particular, that a majority of secular terms (and the corresponding terms in the renormalization flow equations) that could be present on general grounds given the spectrum of frequencies of linear AdS perturbations, do not in fact arise.
v2: 32 pages, substantial comments added, references added, minor typos corrected
References in corpus (11)
- FORM version 4.0
- On weakly turbulent instability of anti-de Sitter space
- Boson Stars in AdS
- 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
- Time-periodic solutions in Einstein AdS - massless scalar field system
- What drives AdS unstable?
- Holographic Relaxation of Finite Size Isolated Quantum Systems
- Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon
- Holographic interpretation of renormalization group approach to singular perturbations in non-linear differential equations
Cited by in corpus (91)
- Numerical Methods for Finding Stationary Gravitational Solutions
- Renormalization, averaging, conservation laws and AdS (in)stability
- Resonant dynamics and the instability of anti-de Sitter spacetime
- Universality in fast quantum quenches
- Hairy black holes and the endpoint of AdS charged superradiance
- Conserved quantities and dual turbulent cascades in Anti-de Sitter spacetime
- Islands of stability and recurrence times in AdS
- A Hidden Symmetry of AdS Resonances
- Nonlinear stability in nonlocal gravity
- The missing top of AdS resonance structure
- Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates
- Position space analysis of the AdS (in)stability problem
- AdS perturbations, isometries, selection rules and the Higgs oscillator
- Delayed collapses of BECs in relation to AdS gravity
- AdS (In)stability: Lessons From The Scalar Field
- Ultraviolet asymptotics and singular dynamics of AdS perturbations
- AdS (in)stability: an analytic approach
- Collapse and Nonlinear Instability of AdS with Angular Momenta
- Gravitational geons in asymptotically anti-de Sitter spacetimes
- Self-gravitating scalar breathers with negative cosmological constant
- Bounds on quantum evolution complexity via lattice cryptography
- Conditionally Extended Validity of Perturbation Theory: Persistence of AdS Stability Islands
- Two infinite families of resonant solutions for the Gross-Pitaevskii equation
- A proof of the instability of AdS for the Einstein--null dust system with an inner mirror
- Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
- AdS nonlinear instability: moving beyond spherical symmetry
- Phases of Global AdS Black Holes
- Higher order perturbations of Anti-de Sitter space and time-periodic solutions of vacuum Einstein equations
- Solvable cubic resonant systems
- Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations
- Thermalization with chemical potentials, and higher spin black holes
- Nonlinear stability of Minkowski spacetime in Nonlocal Gravity
- Maximally rotating waves in AdS and on spheres
- A nonrelativistic limit for AdS perturbations
- Anti-de Sitter geon families
- Quantum resonant systems, integrable and chaotic
- De Sitter bubbles from anti-de Sitter fluctuations
- Time-periodic solutions of massive scalar fields in AdS background: perturbative constructions
- Klein-Gordonization: mapping superintegrable quantum mechanics to resonant spacetimes
- Gravitational collapse of massless scalar field in gravity
- Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap
- A Stochasticity Threshold in Holography and and the Instability of AdS
- Necessary conditions for an AdS-type instability
- Classes of Stable Initial Data for Massless and Massive Scalars in Anti-de Sitter Spacetime
- Charting the AdS Islands of Stability with Multi-oscillators?
- Collapse of self-interacting scalar field in anti-de Sitter space
- Superradiant instability of black resonators and geons
- Two worlds collide: Interacting shells in AdS spacetime and chaos
- Complex plane representations and stationary states in cubic and quintic resonant systems
- Time-evolution of holographic entanglement entropy and metric perturbations
- Energy level splitting for weakly interacting bosons in a harmonic trap
- Black Hole Formation in AdS Einstein-Gauss-Bonnet Gravity
- Fully resonant scalars on asymptotically AdS wormholes
- Energy returns in global AdS_4
- AdS nonlinear instability: breaking spherical and axial symmetries
- Coherent Cascade Conjecture for Collapsing Solutions in Global AdS
- Hidden symmetries of the Higgs oscillator and the conformal algebra
- Universality of non-equilibrium dynamics of CFTs from holography
- Turbulent cascades in a truncation of the cubic Szego equation and related systems
- Breathing modes, quartic nonlinearities and effective resonant systems
- Gauge dependence of the AdS instability problem
- Existence of quasinormal modes for Kerr-AdS black holes
- On turbulence for spacetimes with stable trapping
- On the stability of anti-de Sitter spacetime
- Melonic Turbulence
- New islands of stability with double-trace deformations
- Detailed ultraviolet asymptotics for AdS scalar field perturbations
- Fast and Slow Coherent Cascades in Anti-de Sitter Spacetime
- Time-periodicities in holographic CFTs
- AdS instability: resonant system for gravitational perturbations of AdS in the cohomogeneity-two biaxial Bianchi IX ansatz
- Examining Instabilities Due to Driven Scalars in AdS
- Collisions of massive particles, timelike thin shells and formation of black holes in three dimensions
- Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems
- Thermal equilibrium states and instability of self-gravitating particles in an asymptotically AdS spacetime
- Complexity of Scalar Collapse in Anti-de Sitter Spacetime
- Resonant Dynamics and the Instability of the Box Minkowski Model
- Phase Diagram of Stability for Massive Scalars in Anti-de Sitter Spacetime
- Gravitational systems in asymptotically anti-de Sitter space-times
- First return times on sparse random graphs
- New Limits for Large Matrix and Tensor Models: Large , Melons and Applications
- Scalar collapse in AdS with an OpenCL open source code
- Universal turbulence on branes in holography
- Energy cascades and condensation via coherent dynamics in Hamiltonian systems
- Non-linear periodic waves on the Einstein cylinder
- Gravitational Perturbations in a cavity: Nonlinearities
- Gravothermal catastrophe and critical dimension in a -dimensional asymptotically AdS spacetime
- Nonlinear perturbations of higher dimensional anti-de Sitter spacetime
- A superintegrable quantum field theory
- On relation between renormalized frequency and heat capacity for particles in an anharmonic potential
- Einstein-Vlasov system with equal-angular momenta in
- Dynamics of a nonminimally coupled scalar field in asymptotically spacetime