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On Feynman rules for Mellin amplitudes in AdS/CFT

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Abstract

The computation of CFT correlation functions via Witten diagrams in AdS space can be simplified via the Mellin transform. Recently a set of Feynman rules for tree-level Mellin space amplitudes has been proposed for scalar theories. In this note we derive these rules by explicitly evaluating all of the relevant Witten diagram integrals for the scalar φn theory. We also check that the rules reduce to the usual Feynman rules in the flat space limit.

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References

  1. J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1133] [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  2. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  3. S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  4. H. Liu and A.A. Tseytlin, On four point functions in the CFT/AdS correspondence, Phys. Rev. D 59 (1999) 086002 [hep-th/9807097] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  5. H. Liu, Scattering in anti-de Sitter space and operator product expansion, Phys. Rev. D 60 (1999) 106005 [hep-th/9811152] [INSPIRE].

    ADS  Google Scholar 

  6. E. D’Hoker and D.Z. Freedman, General scalar exchange in AdS(d + 1), Nucl. Phys. B 550 (1999) 261 [hep-th/9811257] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  7. D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Comments on 4 point functions in the CFT/AdS correspondence, Phys. Lett. B 452 (1999) 61 [hep-th/9808006] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  8. D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d)/AdS(d + 1) correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  10. G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N = 4 SYM(4) in supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. G. Arutyunov, F. Dolan, H. Osborn and E. Sokatchev, Correlation functions and massive Kaluza-Klein modes in the AdS/CFT correspondence, Nucl. Phys. B 665 (2003) 273 [hep-th/0212116] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. G. Arutyunov and E. Sokatchev, On a large-N degeneracy in N = 4 SYM and the AdS/CFT correspondence, Nucl. Phys. B 663 (2003) 163 [hep-th/0301058] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. L. Berdichevsky and P. Naaijkens, Four-point functions of different-weight operators in the AdS/CFT correspondence, JHEP 01 (2008) 071 [arXiv:0709.1365] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. L.I. Uruchurtu, Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence, JHEP 03 (2009) 133 [arXiv:0811.2320] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. E. Buchbinder and A. Tseytlin, On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT, JHEP 08 (2010) 057 [arXiv:1005.4516] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. L.I. Uruchurtu, Next-next-to-extremal Four Point Functions of N = 4 1/2 BPS Operators in the AdS/CFT Correspondence, JHEP 08 (2011) 133 [arXiv:1106.0630] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. F. Dolan, M. Nirschl and H. Osborn, Conjectures for large-N superconformal N = 4 chiral primary four point functions, Nucl. Phys. B 749 (2006) 109 [hep-th/0601148] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. E. D’Hoker, D.Z. Freedman and L. Rastelli, AdS/CFT four point functions: How to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th/9905049] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  19. S. Raju, BCFW for Witten Diagrams, Phys. Rev. Lett. 106 (2011) 091601 [arXiv:1011.0780] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. S. Raju, Recursion Relations for AdS/CFT Correlators, Phys. Rev. D 83 (2011) 126002 [arXiv:1102.4724] [INSPIRE].

    ADS  Google Scholar 

  21. G. Mack, D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes, arXiv:0907.2407 [INSPIRE].

  22. G. Mack, D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models, arXiv:0909.1024 [INSPIRE].

  23. J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. M.F. Paulos, Towards Feynman rules for Mellin amplitudes, JHEP 10 (2011) 074 DOI:dx.doi.org [arXiv:1107.1504] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. A.L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B.C. van Rees, A Natural Language for AdS/CFT Correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [INSPIRE].

    Article  ADS  Google Scholar 

  26. M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Blocks, JHEP 11 (2011) 154 [arXiv:1109.6321] [INSPIRE].

    Article  ADS  Google Scholar 

  28. I. Balitsky, Mellin representation of the graviton bulk-to-bulk propagator in AdS, Phys. Rev. D 83 (2011) 087901 [arXiv:1102.0577] [INSPIRE].

    ADS  Google Scholar 

  29. L. Susskind, Holography in the flat space limit, hep-th/9901079 [INSPIRE].

  30. J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].

  31. M. Gary, S.B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80 (2009) 085005 [arXiv:0903.4437]. 24 pages, 3 figs [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  32. I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. A.L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective Conformal Theory and the Flat-Space Limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. T. Okuda and J. Penedones, String scattering in flat space and a scaling limit of Yang-Mills correlators, Phys. Rev. D 83 (2011) 086001 [arXiv:1002.2641] [INSPIRE].

    ADS  Google Scholar 

  35. A.L. Fitzpatrick and J. Kaplan, Scattering States in AdS/CFT, arXiv:1104.2597 [INSPIRE].

  36. M. Gary and S.B. Giddings, The Flat space S-matrix from the AdS/CFT correspondence?, Phys. Rev. D 80 (2009) 046008 [arXiv:0904.3544] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  37. S.B. Giddings, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61 (2000) 106008 [hep-th/9907129] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  38. M. Gary and S.B. Giddings, Constraints on a fine-grained AdS/CFT correspondence, arXiv:1106.3553 [INSPIRE].

  39. K. Symanzik, On Calculations in conformal invariant field theories, Lett. Nuovo Cim. 3 (1972) 734 [INSPIRE].

  40. A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, arXiv:1111.6972 [INSPIRE].

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Authors and Affiliations

  1. Physics Department, Brown University, Providence, Rhode Island, 02912, U.S.A

    Dhritiman Nandan & Anastasia Volovich

  2. Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom

    Congkao Wen

Authors
  1. Dhritiman Nandan
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  2. Anastasia Volovich
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  3. Congkao Wen
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Correspondence to Congkao Wen.

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ArXiv ePrint: 1112.0305

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Nandan, D., Volovich, A. & Wen, C. On Feynman rules for Mellin amplitudes in AdS/CFT. J. High Energ. Phys. 2012, 129 (2012). https://doi.org/10.1007/JHEP05(2012)129

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  • DOI: https://doi.org/10.1007/JHEP05(2012)129

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