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.

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

References in corpus (4)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• Conformal coupling of the scalar field with gravity in higher dimensions and invariant powers of the Laplacian

Cited by in corpus (4)

• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• Weyl-Ambient Geometries
• Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians