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Journal of High Energy Physics

, 2019:247 | Cite as

20′ five-point function from AdS5× S5 supergravity

  • Vasco Gonçalves
  • Raul Pereira
  • Xinan ZhouEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We develop new techniques to compute five-point correlation functions from IIB supergravity on AdS5 × S5. Our methods rely entirely on symmetry and general con- sistency conditions, and eschew detailed knowledge of the supergravity effective action. We demonstrate our methods by computing the five-point function of the 20 operator, which is the superconformal primary of the stress tensor multiplet. We also develop systematic methods to compute the five-point conformal blocks in series expansions. Using the ex- plicit expressions of the conformal blocks, we perform a Euclidean OPE analysis of the 20 five-point function. We find expected agreement with non-renormalized quantities and also extract new CFT data at strong coupling.

Keywords

AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Supplementary material

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ESM 1 (TGZ 2457 kb)

References

  1. [1]
    L. Rastelli and X. Zhou, Mellin amplitudes for AdS 5 × S 5 , Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].CrossRefADSGoogle Scholar
  2. [2]
    L. Rastelli and X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP 04 (2018) 014 [arXiv:1710.05923] [INSPIRE].CrossRefMathSciNetzbMATHGoogle Scholar
  3. [3]
    G. Arutyunov, S. Frolov, R. Klabbers and S. Savin, Towards 4-point correlation functions of any 1 -BPS operators from supergravity, JHEP 04 (2017) 005 [arXiv:1701.00998] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  4. [4]
    G. Arutyunov, R. Klabbers and S. Savin, Four-point functions of all-different-weight chiral primary operators in the supergravity approximation, JHEP 09 (2018) 023 [arXiv:1806.09200] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  5. [5]
    G. Arutyunov, R. Klabbers and S. Savin, Four-point functions of 1/2-BPS operators of any weights in the supergravity approximation, JHEP 09 (2018) 118 [arXiv:1808.06788] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  6. [6]
    L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS 5 × S 5 , Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Quantum Gravity from Conformal Field Theory, JHEP 01 (2018) 035 [arXiv:1706.02822] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  8. [8]
    F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Unmixing Supergravity, JHEP 02 (2018) 133 [arXiv:1706.08456] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  9. [9]
    F. Aprile, J. Drummond, P. Heslop and H. Paul, Double-trace spectrum of N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 98 (2018) 126008 [arXiv:1802.06889] [INSPIRE].ADSMathSciNetGoogle Scholar
  10. [10]
    O. Aharony, L.F. Alday, A. Bissi and E. Perlmutter, Loops in AdS from Conformal Field Theory, JHEP 07 (2017) 036 [arXiv:1612.03891] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  11. [11]
    L.F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, JHEP 12 (2018) 017 [arXiv:1711.02031] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  12. [12]
    F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Loop corrections for Kaluza-Klein AdS amplitudes, JHEP 05 (2018) 056 [arXiv:1711.03903] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  13. [13]
    S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  14. [14]
    L.F. Alday, On Genus-one String Amplitudes on AdS 5 × S 5 , arXiv:1812.11783 [INSPIRE].
  15. [15]
    L.F. Alday, A. Bissi and E. Perlmutter, Genus-One String Amplitudes from Conformal Field Theory, JHEP 06 (2019) 010 [arXiv:1809.10670] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  16. [16]
    D.J. Binder, S.M. Chester, S.S. Pufu and Y. Wang, \( \mathcal{N} \) = 4 Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization, arXiv:1902.06263 [INSPIRE].
  17. [17]
    V. Gonçalves, Four point function of \( \mathcal{N} \) = 4 stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [INSPIRE].
  18. [18]
    X. Zhou, On Superconformal Four-Point Mellin Amplitudes in Dimension d > 2, JHEP 08 (2018) 187 [arXiv:1712.02800] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  19. [19]
    L. Rastelli and X. Zhou, Holographic Four-Point Functions in the (2, 0) Theory, JHEP 06 (2018) 087 [arXiv:1712.02788] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  20. [20]
    P. Heslop and A.E. Lipstein, M-theory Beyond The Supergravity Approximation, JHEP 02 (2018) 004 [arXiv:1712.08570] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  21. [21]
    S.M. Chester, AdS 4 /C F T 3 for unprotected operators, JHEP 07 (2018) 030 [arXiv:1803.01379] [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    X. Zhou, On Mellin Amplitudes in SCFTs with Eight Supercharges, JHEP 07 (2018) 147 [arXiv:1804.02397] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  23. [23]
    S.M. Chester, S.S. Pufu and X. Yin, The M-theory S-matrix From ABJM: Beyond 11D Supergravity, JHEP 08 (2018) 115 [arXiv:1804.00949] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  24. [24]
    S.M. Chester and E. Perlmutter, M-Theory Reconstruction from (2, 0) CFT and the Chiral Algebra Conjecture, JHEP 08 (2018) 116 [arXiv:1805.00892] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  25. [25]
    D.J. Binder, S.M. Chester and S.S. Pufu, Absence of D 4 R 4 in M-theory From ABJM, arXiv:1808.10554 [INSPIRE].
  26. [26]
    S. Giusto, R. Russo and C. Wen, Holographic correlators in AdS 3, JHEP 03 (2019) 096 [arXiv:1812.06479] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  27. [27]
    T. Abl, P. Heslop and A.E. Lipstein, Recursion relations for anomalous dimensions in the 6d (2, 0) theory, JHEP 04 (2019) 038 [arXiv:1902.00463] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  28. [28]
    L. Rastelli, K. Roumpedakis and X. Zhou, AdS 3 × S 3 Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry, JHEP 10 (2019) 140 [arXiv:1905.11983] [INSPIRE].CrossRefGoogle Scholar
  29. [29]
    S. Giusto, R. Russo, A. Tyukov and C. Wen, Holographic correlators in AdS3 without Witten diagrams, JHEP 09 (2019) 030 [arXiv:1905.12314] [INSPIRE].CrossRefADSGoogle Scholar
  30. [30]
    S. Caron-Huot and A.-K. Trinh, All tree-level correlators in AdS 5 × S 5 supergravity: hidden ten-dimensional conformal symmetry, JHEP 01 (2019) 196 [arXiv:1809.09173] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  31. [31]
    E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Extremal correlators in the AdS/CFT correspondence, hep-th/9908160 [INSPIRE].
  32. [32]
    M. Bianchi and S. Kovacs, Nonrenormalization of extremal correlators in N = 4 SYM theory, Phys. Lett. B 468 (1999) 102 [hep-th/9910016] [INSPIRE].CrossRefADSGoogle Scholar
  33. [33]
    B. Eden, P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Extremal correlators in four-dimensional SCFT, Phys. Lett. B 472 (2000) 323 [hep-th/9910150] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  34. [34]
    J. Erdmenger and M. Pérez-Victoria, Nonrenormalization of next-to-extremal correlators in N = 4 SYM and the AdS/CFT correspondence, Phys. Rev. D 62 (2000) 045008 [hep-th/9912250] [INSPIRE].ADSGoogle Scholar
  35. [35]
    B.U. Eden, P.S. Howe, E. Sokatchev and P.C. West, Extremal and next-to-extremal n point correlators in four-dimensional SCFT, Phys. Lett. B 494 (2000) 141 [hep-th/0004102] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  36. [36]
    E. D’Hoker, J. Erdmenger, D.Z. Freedman and M. Pérez-Victoria, Near extremal correlators and vanishing supergravity couplings in AdS/CFT, Nucl. Phys. B 589 (2000) 3 [hep-th/0003218] [INSPIRE].
  37. [37]
    V. Gonçalves, J. Penedones and E. Trevisani, Factorization of Mellin amplitudes, JHEP 10 (2015) 040 [arXiv:1410.4185] [INSPIRE].
  38. [38]
    C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees, Infinite Chiral Symmetry in Four Dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  39. [39]
    N. Drukker and J. Plefka, Superprotected n-point correlation functions of local operators in N = 4 super Yang-Mills, JHEP 04 (2009) 052 [arXiv:0901.3653] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  40. [40]
    B. Eden, A.C. Petkou, C. Schubert and E. Sokatchev, Partial nonrenormalization of the stress tensor four point function in N = 4 SYM and AdS/CFT, Nucl. Phys. B 607 (2001) 191 [hep-th/0009106] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  41. [41]
    M. Nirschl and H. Osborn, Superconformal Ward identities and their solution, Nucl. Phys. B 711 (2005) 409 [hep-th/0407060] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  42. [42]
    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].
  43. [43]
    G. Mack, D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models, Bulg. J. Phys. 36 (2009) 214 [arXiv:0909.1024] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  44. [44]
    J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  45. [45]
    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].CrossRefADSMathSciNetzbMATHGoogle Scholar
  46. [46]
    M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  47. [47]
    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].CrossRefADSMathSciNetzbMATHGoogle Scholar
  48. [48]
    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky and E. Sokatchev, N = 4 superconformal Ward identities for correlation functions, Nucl. Phys. B 904 (2016) 176 [arXiv:1409.2502] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  49. [49]
    Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated one loop integrals, Phys. Lett. B 302 (1993) 299 [Erratum ibid. B 318 (1993) 649] [hep-ph/9212308] [INSPIRE].
  50. [50]
    Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [INSPIRE].
  51. [51]
    N. Abel, Note sur la fonction \( \psi x=x+\frac{x^2}{2^2}+\frac{x^3}{3^2}+\dots +\frac{n^2}{n^2}+\dots \) , in (Euvres complétes de Niels Henrik Abel — Nouvellé edition, L. Sylow and S. Lie eds., no. 189–193 (1881).Google Scholar
  52. [52]
    S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large N , Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].CrossRefMathSciNetzbMATHGoogle Scholar
  53. [53]
    B. Eden and E. Sokatchev, On the OPE of 1/2 BPS short operators in N = 4 SC F T4 , Nucl. Phys. B 618 (2001) 259 [hep-th/0106249] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  54. [54]
    F.A. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  55. [55]
    A.V. Ryzhov, Quarter BPS operators in N = 4 SYM, JHEP 11 (2001) 046 [hep-th/0109064] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  56. [56]
    E. D’Hoker, P. Heslop, P. Howe and A.V. Ryzhov, Systematics of quarter BPS operators in N = 4 SYM, JHEP 04 (2003) 038 [hep-th/0301104] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  57. [57]
    E. D’Hoker and A.V. Ryzhov, Three point functions of quarter BPS operators in N = 4 SYM, JHEP 02 (2002) 047 [hep-th/0109065] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  58. [58]
    M. Bianchi, S. Kovacs, G. Rossi and Y.S. Stanev, Properties of the Konishi multiplet in N = 4 SYM theory, JHEP 05 (2001) 042 [hep-th/0104016] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  59. [59]
    G. Arutyunov, S. Frolov and A.C. Petkou, Operator product expansion of the lowest weight CPOs in \( \mathcal{N} \) = 4 SY M 4 at strong coupling, Nucl. Phys. B 586 (2000) 547 [Erratum ibid. B 609 (2001) 539] [hep-th/0005182] [INSPIRE].
  60. [60]
    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].CrossRefADSMathSciNetzbMATHGoogle Scholar
  61. [61]
    K.A. Intriligator, Bonus symmetries of N = 4 superYang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  62. [62]
    K.A. Intriligator and W. Skiba, Bonus symmetry and the operator product expansion of N = 4 SuperYang-Mills, Nucl. Phys. B 559 (1999) 165 [hep-th/9905020] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  63. [63]
    B. Eden, P.S. Howe and P.C. West, Nilpotent invariants in N = 4 SYM, Phys. Lett. B 463 (1999) 19 [hep-th/9905085] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  64. [64]
    A. Petkou and K. Skenderis, A Nonrenormalization theorem for conformal anomalies, Nucl. Phys. B 561 (1999) 100 [hep-th/9906030] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  65. [65]
    P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Explicit construction of nilpotent covariants in N = 4 SYM, Nucl. Phys. B 571 (2000) 71 [hep-th/9910011] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  66. [66]
    P.J. Heslop and P.S. Howe, OPEs and three-point correlators of protected operators in N = 4 SYM, Nucl. Phys. B 626 (2002) 265 [hep-th/0107212] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  67. [67]
    M. Baggio, J. de Boer and K. Papadodimas, A non-renormalization theorem for chiral primary 3-point functions, JHEP 07 (2012) 137 [arXiv:1203.1036] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  68. [68]
    P.J. Heslop and P.S. Howe, Aspects of N = 4 SYM, JHEP 01 (2004) 058 [hep-th/0307210] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  69. [69]
    N. Drukker and J. Plefka, The Structure of n-point functions of chiral primary operators in N = 4 super Yang-Mills at one-loop, JHEP 04 (2009) 001 [arXiv:0812.3341] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  70. [70]
    R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  71. [71]
    C. Beem, L. Rastelli and B.C. van Rees, \( \mathcal{W} \) symmetry in six dimensions, JHEP 05 (2015) 017 [arXiv:1404.1079] [INSPIRE].
  72. [72]
    V. Rosenhaus, Multipoint Conformal Blocks in the Comb Channel, JHEP 02 (2019) 142 [arXiv:1810.03244] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  73. [73]
    J.-F. Fortin and W. Skiba, New Methods for Conformal Correlation Functions, arXiv:1905.00434 [INSPIRE].
  74. [74]
    F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  75. [75]
    M. Hogervorst and S. Rychkov, Radial Coordinates for Conformal Blocks, Phys. Rev. D 87 (2013) 106004 [arXiv:1303.1111] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.ICTP South American Institute for Fundamental ResearchIFT-UNESPSão PauloBrazil
  2. 2.School of Mathematics and Hamilton Mathematics InstituteTrinity College DublinDublin 2Ireland
  3. 3.Princeton Center for Theoretical SciencePrinceton UniversityPrincetonU.S.A.

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