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We revisit the calculation of holographic correlation functions in IIB supergravity on $AdS_5\times S^5$.
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G. Arutyunov and E. Sokatchev, Nucl. Phys. B663
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Note that τ 𝒪 \tau_{\cal O} is an integer with the same parity as p 1 + p 2 p_{1}+p_{2} and p 3 + p 4 p_{3}+p_{4} , see Table 1 of Dolan and Osborn 2003
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M. S. Costa, V. Goncalves, and J. Penedones, JHEP 12
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This truncation can be seen from the explicit expressions in Costa et al. 2012 and is equivalent to the observation in D’Hoker et al. 1999b that the exchange Witten diagrams relevant for A d S 5 × S 5 AdS_{5}\times S^{5} supergravity can always be written as finite sums of contact diagrams
2012
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A BCFW-inspired formalism for holographic correlators has been developed in momentum space Raju 2011 ; Raju 2012
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M. Baggio, J. de Boer, and K. Papadodimas, JHEP 07
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A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju, and B. C. van Rees, JHEP 11
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2011
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Happily, in all explicit supergravity calculations performed so far Arutyunov and Frolov 2000b ; Arutyunov et al. 2003 ; Arutyunov and Sokatchev 2003 ; Berdichevsky and Naaijkens 2008 ; Uruchurtu 2009 ; Uruchurtu 2011 the contribution of vertices with four spacetime derivatives can be effectively re-written in terms of vertices with zero or two derivatives. It would be nice to prove that this reduction of order occurs in the general case, as we have argued indirectly from compatibility with the flat space limit. We are indebted to G. Arutyunov and S. Frolov for a very useful discussion on this point
2011
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2011
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Three-point correlators of arbitrary one-half BPS operators were computed in the early days of AdS/CFT Freedman et al. 1999 ; Lee et al. 1998 and found to agree with the tree-level SYM results, a fact subsequently explained by a non-renormalization theorem, see, e.g
2012
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2012
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2013
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See, e.g
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V. Gonçalves, J. Penedones, and E. Trevisani, JHEP 10
2015
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L. F. Alday and A. Bissi, JHEP 02
2015
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H. Elvang and Y.-t. Huang, Scattering Amplitudes in Gauge Theory and Gravity (Cambridge University Press, 2015)
2015
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L. F. Alday and A. Bissi, (2016), arXiv:1606.09593 [hep-th]
2016
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Results for general weights p i p_{i} are available up to order O ( λ 3 ) O(\lambda^{3}) Chicherin et al. 2016
2016
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D. Chicherin, J. Drummond, P. Heslop, and E. Sokatchev, JHEP 08
2016
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