Abstract
We compute the holographic stress tensor and the logarithmic energy-momentum tensor of Einstein-Weyl gravity at the critical point. This computation is carried out performing a holographic expansion in a bulk action supplemented by the Gauss-Bonnet term with a fixed coupling. The renormalization scheme defined by the addition of this topological term has the remarkable feature that all Einstein modes are identically cancelled both from the action and its variation. Thus, what remains comes from a nonvanishing Bach tensor, which accounts for non-Einstein modes associated to logarithmic terms which appear in the expansion of the metric. In particular, we compute the holographic 1-point functions for a generic boundary geometric source.
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References
M.H. Goroff and A. Sagnotti, The Ultraviolet Behavior of Einstein Gravity, Nucl. Phys. B 266 (1986) 709 [INSPIRE].
K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
S.L. Adler, Einstein Gravity as a Symmetry Breaking Effect in Quantum Field Theory, Rev. Mod. Phys. 54 (1982) 729 [Erratum ibid. 55 (1983) 837] [INSPIRE].
K.S. Stelle, Classical Gravity with Higher Derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
S. Deser and B. Tekin, Massive, topologically massive, models, Class. Quant. Grav. 19 (2002) L97 [hep-th/0203273] [INSPIRE].
H. Lü and C.N. Pope, Critical Gravity in Four Dimensions, Phys. Rev. Lett. 106 (2011) 181302 [arXiv:1101.1971] [INSPIRE].
G. Anastasiou, R. Olea and D. Rivera-Betancour, Noether-Wald energy in Critical Gravity, arXiv:1707.00341 [INSPIRE].
J. Maldacena, Einstein Gravity from Conformal Gravity, arXiv:1105.5632 [INSPIRE].
G. Anastasiou and R. Olea, From conformal to Einstein Gravity, Phys. Rev. D 94 (2016) 086008 [arXiv:1608.07826] [INSPIRE].
M. Alishahiha and R. Fareghbal, D-Dimensional Log Gravity, Phys. Rev. D 83 (2011) 084052 [arXiv:1101.5891] [INSPIRE].
E.A. Bergshoeff, O. Hohm, J. Rosseel and P.K. Townsend, Modes of Log Gravity, Phys. Rev. D 83 (2011) 104038 [arXiv:1102.4091] [INSPIRE].
I. Gullu, M. Gurses, T.C. Sisman and B. Tekin, AdS Waves as Exact Solutions to Quadratic Gravity, Phys. Rev. D 83 (2011) 084015 [arXiv:1102.1921] [INSPIRE].
V. Gurarie, Logarithmic operators in conformal field theory, Nucl. Phys. B 410 (1993) 535 [hep-th/9303160] [INSPIRE].
J.S. Caux, I.I. Kogan and A.M. Tsvelik, Logarithmic operators and hidden continuous symmetry in critical disordered models, Nucl. Phys. B 466 (1996) 444 [hep-th/9511134] [INSPIRE].
N. Johansson, A. Naseh and T. Zojer, Holographic two-point functions for 4d log-gravity, JHEP 09 (2012) 114 [arXiv:1205.5804] [INSPIRE].
O. Mišković, R. Olea and M. Tsoukalas, Renormalized AdS action and Critical Gravity, JHEP 08 (2014) 108 [arXiv:1404.5993] [INSPIRE].
S.W. MacDowell and F. Mansouri, Unified Geometric Theory of Gravity and Supergravity, Phys. Rev. Lett. 38 (1977) 739 [Erratum ibid. 38 (1977) 1376] [INSPIRE].
R. Olea, Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes, JHEP 06 (2005) 023 [hep-th/0504233] [INSPIRE].
O. Mišković and R. Olea, Topological regularization and self-duality in four-dimensional anti-de Sitter gravity, Phys. Rev. D 79 (2009) 124020 [arXiv:0902.2082] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
H. Lü, Y. Pang and C.N. Pope, Conformal Gravity and Extensions of Critical Gravity, Phys. Rev. D 84 (2011) 064001 [arXiv:1106.4657] [INSPIRE].
M. Porrati and M.M. Roberts, Ghosts of Critical Gravity, Phys. Rev. D 84 (2011) 024013 [arXiv:1104.0674] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
D. Grumiller and N. Johansson, Consistent boundary conditions for cosmological topologically massive gravity at the chiral point, Int. J. Mod. Phys. D 17 (2009) 2367 [arXiv:0808.2575] [INSPIRE].
M. Alishahiha and A. Naseh, Holographic renormalization of new massive gravity, Phys. Rev. D 82 (2010) 104043 [arXiv:1005.1544] [INSPIRE].
K. Skenderis, M. Taylor and B.C. van Rees, Topologically Massive Gravity and the AdS/CFT Correspondence, JHEP 09 (2009) 045 [arXiv:0906.4926] [INSPIRE].
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Anastasiou, G., Olea, R. Holographic correlation functions in Critical Gravity. J. High Energ. Phys. 2017, 19 (2017). https://doi.org/10.1007/JHEP11(2017)019
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DOI: https://doi.org/10.1007/JHEP11(2017)019