2007/07/31 by Ruben Manvelyan, Karapet Mkrtchyan, R. L. Mkrtchyan +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #hep-th
paper · pdf · doi:10.1016/j.physletb.2007.10.014
published as Phys.Lett.B657:112-119,2007 · 15 pages, Latex, v.2 references added, v.3 ref. added, to appear in Phys. Lett. B
arxiv created 2007/10/10 · openalex publication_date 2007/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The hierarchy of conformally invariant k th powers of the Laplacian acting on a scalar field with scaling dimensions Δ ( k ) = k − d / 2 , k = 1 , 2 , 3 , as obtained in the recent work [R. Manvelyan, D.H. Tchrakian, Phys. Lett. B 644 (2007) 370, hep-th/0611077 ] is rederived using the Fefferman–Graham ( d + 2 ) -dimensional ambient space approach. The corresponding mysterious “holographic” structure of these operators is clarified. We explore also the ( d + 2 ) -dimensional ambient space origin of the Ricci gauging procedure proposed by A. Iorio, L. O'Raifeartaigh, I. Sachs and C. Wiesendanger as another method of constructing the Weyl invariant Lagrangians. The corresponding gauged ambient metric, Fefferman–Graham expansion and extended Penrose–Brown–Henneaux transformations are proposed and analyzed.