Conformal invariant powers of the Laplacian, Fefferman-Graham ambient metric and Ricci gauging

Abstract

The hierarchy of conformally invariant k-th powers of the Laplacian acting on a scalar field with scaling dimensions ${\Delta }_{(k)}=k-d/2$, k=1,2,3 as obtained in the recent work [1] 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 \emph{gauged} ambient metric, Fefferman-Graham expansion and extended Penrose-Brown-Henneaux transformations are proposed and analyzed.

arXiv comment15 pages, Latex, v.2 references added, v.3 ref. added, to appear in Phys. Lett. B

References in corpus (18)

• The Holographic Weyl anomaly
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Asymptotically Anti-de Sitter spacetimes and their stress energy tensor
• Holography and the Weyl anomaly
• Diffeomorphisms and Holographic Anomalies
• Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence
• Weyl-Gauging and Conformal Invariance
• Conformally Covariant Differential Operators: Properties and Applications
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• Diffeomorphisms, Anomalies and the Fefferman-Graham Ambiguity
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• A classification of local Weyl invariants in D=8
• A Weyl-covariant tensor calculus
• Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups
• Conformal coupling of the scalar field with gravity in higher dimensions and invariant powers of the Laplacian
• Rudiments of Holography
• The Dirichlet Obstruction in AdS/CFT

Cited by in corpus (10)

• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• Shift Symmetries in (Anti) de Sitter Space
• Partially-massless higher-spin algebras and their finite-dimensional truncations
• Polyakov formulas for GJMS operators from AdS/CFT
• Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly
• Weyl-Ambient Geometries
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all
• Constructing conformally invariant equations by using Weyl geometry
• Examining Instabilities Due to Driven Scalars in AdS