Abstract
We consider holography of two $pp$-wave metrics in conformal gravity, their one-point functions, and asymptotic symmetries. One of the metrics is a generalization of the standard $pp$ waves in Einstein gravity to conformal gravity. The holography of this metric shows that within conformal gravity one can have a realized solution which has a nonvanishing partially massless response tensor even for a vanishing subleading term in the Fefferman-Graham expansion (i.e., Neumann boundary conditions) and vice versa.
Highlights
Conformal gravity (CG) is a higher derivative theory of gravity which has a recurrent appearance in literature
There is no classification of the global cosmological solutions in CG; a number of Einstein gravity (EG) solutions have been generalized to CG [8,9]
We have studied the pp-wave solution of conformal gravity and its symmetries
Summary
Conformal gravity (CG) is a higher derivative theory of gravity which has a recurrent appearance in literature. It is power-counting renormalizable and highly symmetric which makes it interesting for studying [1,2]. CG holography has in the earlier studies showed that in the framework of AdS=CFT there are two holographic stress-energy tensors at the boundary. Holographic analyses of a Schwarzschild solution in EG, ManheimmKazanas-Riegert solution in CG [5], and rotating black hole solution in AdS with Rindler hair [8] showed that their PMR vanishes when generalized Fefferman-Graham boundary conditions reduce to standard Fefferman-Graham boundary conditions used in EG.. Besides the holography of the solution, we consider its Killing vectors, charges, and asymmptotic symmetry algebra (ASA) as well as speculate the possibility of using the metric as a cosmological background for string quantization
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