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Journal of High Energy Physics

, 2013:202 | Cite as

Higher-spin correlators

  • Luis F. Alday
  • Agnese Bissi
Article

Abstract

We analyze the properly normalized three-point correlator of two protected scalar operators and one higher spin twist-two operator in \( \mathcal{N}=4 \) super Yang-Mills, in the limit of large spin j. The relevant structure constant can be extracted from the OPE of the four-point correlator of protected scalar operators. We show that crossing symmetry of the four point correlator plus a judicious guess for the perturbative structure of the three-point correlator, allow to make a prediction for the structure constant at all loops in perturbation theory, up to terms that remain finite as the spin becomes large. Furthermore, the expression for the structure constant allows to propose an expression for the all loops four-point correlator \( \mathcal{G}\left( {u,v} \right) \), in the limit u, v → 0. Our predictions are in perfect agreement with the large j expansion of results available in the literature.

Keywords

Supersymmetric gauge theory Conformal and W Symmetry Discrete and Finite Symmetries 

References

  1. [1]
    N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    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].MathSciNetMATHGoogle Scholar
  3. [3]
    G. Korchemsky, Asymptotics of the Altarelli-Parisi-Lipatov evolution kernels of parton distributions, Mod. Phys. Lett. A 4 (1989) 1257 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    G. Korchemsky and G. Marchesini, Structure function for large x and renormalization of Wilson loop, Nucl. Phys. B 406 (1993) 225 [hep-ph/9210281] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 01 (2007) P01021 [hep-th/0610251] [INSPIRE].CrossRefGoogle Scholar
  6. [6]
    B. Basso, G. Korchemsky and J. Kotanski, Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. Lett. 100 (2008) 091601 [arXiv:0708.3933] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    L.F. Alday, J.R. David, E. Gava and K. Narain, Structure constants of planar N = 4 Yang-Mills at one loop, JHEP 09 (2005) 070 [hep-th/0502186] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    J. Plefka and K. Wiegandt, Three-point functions of twist-two operators in N = 4 SYM at one loop, JHEP 10 (2012) 177 [arXiv:1207.4784] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    V. Kazakov and E. Sobko, Three-point correlators of twist-2 operators in N = 4 SYM at Born approximation, JHEP 06 (2013) 061 [arXiv:1212.6563] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    G. Georgiou, SL(2) sector: weak/strong coupling agreement of three-point correlators, JHEP 09 (2011) 132 [arXiv:1107.1850] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    Y. Kazama and S. Komatsu, On holographic three point functions for GKP strings from integrability, JHEP 01 (2012) 110 [Erratum ibid. 06 (2012) 150] [arXiv:1110.3949] [INSPIRE].
  12. [12]
    Y. Kazama and S. Komatsu, Wave functions and correlation functions for GKP strings from integrability, JHEP 09 (2012) 022 [arXiv:1205.6060] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    F. Dolan and H. Osborn, Conformal partial wave expansions for N = 4 chiral four point functions, Annals Phys. 321 (2006) 581 [hep-th/0412335] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  14. [14]
    B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM, Nucl. Phys. B 862 (2012) 193 [arXiv:1108.3557] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    B. Eden, Three-loop universal structure constants in N = 4 SUSY Yang-Mills theory, arXiv:1207.3112 [INSPIRE].
  16. [16]
    T. Ohrndorf, Constraints from conformal covariance on the mixing of operators of lowest twist, Nucl. Phys. B 198 (1982) 26 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    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 [Erratum ibid. B 609 (2001) 539] [hep-th/0005182] [INSPIRE].
  18. [18]
    F. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    L. Bianchi, V. Forini and A.V. Kotikov, On DIS Wilson coefficients in N = 4 super Yang-Mills theory, Phys. Lett. B 725 (2013) 394 [arXiv:1304.7252] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    G. Korchemsky and G. Marchesini, Resummation of large infrared corrections using Wilson loops, Phys. Lett. B 313 (1993) 433 [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, JHEP 09 (2011) 123 [arXiv:1007.3243] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    Z. Komargodski and A. Zhiboedov, Convexity and liberation at large spin, arXiv:1212.4103 [INSPIRE].
  23. [23]
    A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The analytic bootstrap and AdS superhorizon locality, arXiv:1212.3616 [INSPIRE].
  24. [24]
    A. Kotikov, L. Lipatov, A. Onishchenko and V. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. B 632 (2006) 754] [hep-th/0404092] [INSPIRE].
  25. [25]
    N. Gromov and P. Vieira, Quantum integrability for three-point functions, arXiv:1202.4103 [INSPIRE].
  26. [26]
    M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning conformal blocks, JHEP 11 (2011) 154 [arXiv:1109.6321] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    L.F. Alday and J.M. Maldacena, Comments on operators with large spin, JHEP 11 (2007) 019 [arXiv:0708.0672] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    J. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys. A 14 (1999) 2037 [hep-ph/9806280] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    J. Ablinger, A computer algebra toolbox for harmonic sums related to particle physics, Diploma Thesis, Johannes Kepler University, Germany (2009) [arXiv:1011.1176] [INSPIRE].
  31. [31]
    J. Ablinger, J. Blümlein and C. Schneider, Harmonic sums and polylogarithms generated by cyclotomic polynomials, J. Math. Phys. 52 (2011) 102301 [arXiv:1105.6063] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordU.K.

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