Four point function of \( \mathcal{N}=4 \) stress-tensor multiplet at strong coupling

  • Vasco Gonçalves
Open Access
Regular Article - Theoretical Physics


In this short note we use the flat space limit and the relation between the 4-pt correlation function of the bottom and top components of the stress tensor multiplet to constraint its stringy corrections at strong coupling in the planar limit. Then we use this four point function to compute corrections to the anomalous dimension of double trace operators of the Lagrangian density and to compute energy-energy correlators at strong coupling.


AdS-CFT Correspondence Strong Coupling Expansion 


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.


  1. [1]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    S.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].ADSCrossRefMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    L. Cornalba, M.S. Costa, J. Penedones and R. Schiappa, Eikonal approximation in AdS/CFT: conformal partial waves and finite N four-point functions, Nucl. Phys. B 767 (2007) 327 [hep-th/0611123] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    L. Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange, arXiv:0710.5480 [INSPIRE].
  6. [6]
    L. Cornalba, M.S. Costa and J. Penedones, Eikonal methods in AdS/CFT: BFKL pomeron at weak coupling, JHEP 06 (2008) 048 [arXiv:0801.3002] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    J. Penedones, High energy scattering in the AdS/CFT correspondence, arXiv:0712.0802 [INSPIRE].
  8. [8]
    L. Cornalba, M.S. Costa and J. Penedones, Deep inelastic scattering in conformal QCD, JHEP 03 (2010) 133 [arXiv:0911.0043] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  9. [9]
    M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    M.S. Costa, J. Drummond, V. Goncalves and J. Penedones, The role of leading twist operators in the Regge and Lorentzian OPE limits, JHEP 04 (2014) 094 [arXiv:1311.4886] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    R.C. Brower, M.S. Costa, M. Djurić, T. Raben and C.-I. Tan, Strong coupling expansion for the conformal pomeron/odderon trajectories, JHEP 02 (2015) 104 [arXiv:1409.2730] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    L.F. Alday and A. Bissi, Higher-spin correlators, JHEP 10 (2013) 202 [arXiv:1305.4604] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    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] [INSPIRE].ADSGoogle Scholar
  14. [14]
    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].ADSGoogle Scholar
  15. [15]
    J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
  16. [16]
    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from conformal field theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    V. Gonçalves, J. Penedones and E. Trevisani, Factorization of Mellin amplitudes, arXiv:1410.4185 [INSPIRE].
  19. [19]
    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].ADSGoogle Scholar
  20. [20]
    J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    J.M. Drummond, L. Gallot and E. Sokatchev, Superconformal invariants or how to relate four-point AdS amplitudes, Phys. Lett. B 645 (2007) 95 [hep-th/0610280] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky and E. Sokatchev, N = 4 superconformal Ward identities for correlation functions, arXiv:1409.2502 [INSPIRE].
  23. [23]
    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].ADSCrossRefMATHGoogle Scholar
  24. [24]
    G. Arutyunov, S. Frolov and A.C. Petkou, Operator product expansion of the lowest weight CPOs in N = 4 SYM 4 at strong coupling, Nucl. Phys. B 586 (2000) 547 [hep-th/0005182] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  25. [25]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    A.L. Fitzpatrick and J. Kaplan, Analyticity and the holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    A.V. Kotikov and L.N. Lipatov, Pomeron in the N = 4 supersymmetric gauge model at strong couplings, Nucl. Phys. B 874 (2013) 889 [arXiv:1301.0882] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    N. Gromov, F. Levkovich-Maslyuk, G. Sizov and S. Valatka, Quantum spectral curve at work: from small spin to strong coupling in N = 4 SYM, JHEP 07 (2014) 156 [arXiv:1402.0871] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    R.C. Brower, M. Costa, M. Djuric, T. Raben and C.-I. Tan, Conformal pomeron and odderon in strong coupling, arXiv:1312.1419 [INSPIRE].
  30. [30]
    F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    L. Cornalba, M.S. Costa and J. Penedones, Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion, JHEP 09 (2007) 037 [arXiv:0707.0120] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    N. Gromov, V. Kazakov and P. Vieira, Exact spectrum of planar N = 4 supersymmetric Yang-Mills theory: Konishi dimension at any coupling, Phys. Rev. Lett. 104 (2010) 211601 [arXiv:0906.4240] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    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].
  34. [34]
    G. Mack, D-dimensional conformal field theories with anomalous dimensions as dual resonance models, Bulg. J. Phys. 36 (2009) 214 [arXiv:0909.1024] [INSPIRE].MathSciNetMATHGoogle Scholar
  35. [35]
    A.L. Fitzpatrick and J. Kaplan, Unitarity and the holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    M.S. Costa, V. Gonçalves and J. Penedones, Spinning AdS propagators, JHEP 09 (2014) 064 [arXiv:1404.5625] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  38. [38]
    L.F. Alday, A. Bissi and T. Lukowski, Lessons from crossing symmetry at large-N, arXiv:1410.4717 [INSPIRE].
  39. [39]
    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, From correlation functions to event shapes, Nucl. Phys. B 884 (2014) 305 [arXiv:1309.0769] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, Event shapes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 884 (2014) 206 [arXiv:1309.1424] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  41. [41]
    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, Energy-energy correlations in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 112 (2014) 071601 [arXiv:1311.6800] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  42. [42]
    D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N = 4 SYM, Nucl. Phys. B 862 (2012) 450 [arXiv:1201.5329] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  45. [45]
    B. Eden, C. Schubert and E. Sokatchev, Three loop four point correlator in N = 4 SYM, Phys. Lett. B 482 (2000) 309 [hep-th/0003096] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  46. [46]
    J. Drummond et al., Leading singularities and off-shell conformal integrals, JHEP 08 (2013) 133 [arXiv:1303.6909] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do PortoPortoPortugal

Personalised recommendations