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

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

2007-07-12

arxiv.org/abs/0707.1737v3

Phys.Lett.B657:112-119,2007

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.physletb.2007.10.014

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.

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