2019/12/31 by Bradley Cownden, Brad Cownden
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Geometry #Mathematical physics #Mathematics #Physics #Scalar (mathematics) #Scalar field #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep12(2020)013
v1: 29 pages, 6 figures v2: Added reference and small changes to Discussion. 30 pages, 6 figures v3: To appear in JHEP. Added holographic interpretation, review of resummation procedure, and moved discussion of all-normalizable resonances to appendix. 34 pages, 6 figures
arxiv created 2020/10/13 · openalex publication_date 2020/12/02 · arxiv updated 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract 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 mass values mBF2lt;m2≤ 0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>BF</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo><</mml:mo> <mml:msup> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>≤</mml:mo> <mml:mn>0</mml:mn> </mml:math> , 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.