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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.
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2007
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J. Erdmenger, “Conformally covariant differential operators: Properties and applications,” Class. Quant. Grav. 14
2061
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