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We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes.
1908
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2005
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J. Bergman Ärlebäck, B. Edgar and M. Herberthson, The Bach tensor and other divergence-free tensors , International Journal of Geometric Methods in Modern Physics 2
2005
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R. Olea, Regularization of odd-dimensional AdS gravity: Kounterterms , JHEP 04
2007
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S. Chang, M. Eastwood, B. Orsted and P. C. Yang, What is Q-Curvature? , Acta Appl. Math. 102
2008
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I. Papadimitriou, Holographic renormalization as a canonical transformation , JHEP 11
2010
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M. T. Anderson, L 2 curvature and volume renormalization of the AHE metrics on 4-manifolds , Math. Res. Lett. 8
2001
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S. de Haro, S. N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence , Commun. Math. Phys. 217
2001
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K. A. Meissner and M. Olechowski, Domain walls without cosmological constant in higher order gravity , Phys. Rev. Lett. 86
2001
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C. Fefferman and C. Graham, Q-curvature and Poincaré metrics , Mathematical Research Letters 9
2002
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K. Skenderis, Lecture notes on holographic renormalization , Class. Quant. Grav. 19
2002
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D. Bak, M. Gutperle and S. Hirano, A Dilatonic deformation of AdS(5) and its field theory dual , JHEP 05
2003
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D. Martelli and W. Mueck, Holographic renormalization and Ward identities with the Hamilton-Jacobi method , Nucl. Phys. B654
2003
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2011
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S. F. Ross, Holography for asymptotically locally Lifshitz spacetimes , Class. Quant. Grav. 28
2011
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Y. Ge, G. Wang and J. Wu, The Gauss–Bonnet–Chern Mass of Conformally Flat Manifolds , International Mathematics Research Notices 2014
2013
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2014
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2016
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I. Papadimitriou, Lectures on Holographic Renormalization , Springer Proc. Phys. 176
2016
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2018
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2018
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G. Anastasiou, I. J. Araya and R. Olea, Topological terms, AdS 2n
2018
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2019
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J. Erdmenger, Conformally covariant differential operators: Properties and applications , Class. Quant. Grav. 14
2061
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