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Three-point functions of BMN operators at weak and strong coupling II. One loop matching

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Abstract

In a previous paper JHEP 06 (2012) 142 142 we have shown that the fully dynamical three-point correlation functions of BMN operators are identical at the tree level in the planar limit of perturbative field theory and, on the string theory side, calculated by means of the Dobashi-Yoneya three string vertex in the Penrose limit. Here we present a one-loop calculation of the same quantity both on the field-theory and string-theory side, where a complete identity between the two results is demonstrated.

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References

  1. 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 

  2. M.S. Costa, R. Monteiro, J.E. Santos and D. Zoakos, On three-point correlation functions inthe gauge/gravity duality, JHEP 11 (2010) 141 [arXiv:1008.1070] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. R. Roiban and A. Tseytlin, On semiclassical computation of 3-point functions of closed string vertex operators in AdS 5 × S 5, Phys. Rev. D 82 (2010) 106011 [arXiv:1008.4921] [INSPIRE].

    ADS  Google Scholar 

  4. K. Zarembo, Holographic three-point functions of semiclassical states, JHEP 09 (2010) 030 [arXiv:1008.1059] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. E. Buchbinder and A. Tseytlin, Semiclassical correlators of three states with large S 5 charges in string theory in AdS 5 × S 5, Phys. Rev. D 85 (2012) 026001 arXiv:1110.5621] [INSPIRE].

    ADS  Google Scholar 

  6. M. Michalcik, R.C. Rashkov and M. Schimpf, On semiclassical calculation of three-point functions in AdS 5 × T (1,1), Mod. Phys. Lett. A 27 (2012) 1250091 [arXiv:1107.5795] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. T. Klose and T. McLoughlin, A light-cone approach to three-point functions in AdS 5 × S 5, JHEP 04 (2012) 080 [arXiv:1106.0495] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. G. Georgiou, Two and three-point correlators of operators dual to folded string solutions at strong coupling, JHEP 02 (2011) 046 [arXiv:1011.5181] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. R. Hernandez, Three-point correlation functions from semiclassical circular strings, J. Phys. A 44 (2011) 085403 [arXiv:1011.0408] [INSPIRE].

    ADS  Google Scholar 

  10. D. Arnaudov and R. Rashkov, On semiclassical calculation of three-point functions in AdS 4 × CP 3, Phys. Rev. D 83 (2011) 066011 [arXiv:1011.4669] [INSPIRE].

    ADS  Google Scholar 

  11. C. Park and B.-H. Lee, Correlation functions of magnon and spike, Phys. Rev. D 83 (2011) 126004 [arXiv:1012.3293] [INSPIRE].

    ADS  Google Scholar 

  12. J. Russo and A. Tseytlin, Large spin expansion of semiclassical 3-point correlators in AdS 5 × S 5, JHEP 02 (2011) 029 [arXiv:1012.2760] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. D. Bak, B. Chen and J.-B. Wu, Holographic correlation functions for open strings and branes, JHEP 06 (2011) 014 [arXiv:1103.2024] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. D. Arnaudov, R. Rashkov and T. Vetsov, Three and four-point correlators of operators dual to folded string solutions in AdS 5 × S 5, Int. J. Mod. Phys. A 26 (2011) 3403 [arXiv:1103.6145] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. R. Hernandez, Three-point correlators for giant magnons, JHEP 05 (2011) 123 [arXiv:1104.1160] [INSPIRE].

    Article  ADS  Google Scholar 

  16. X. Bai, B.-H. Lee and C. Park, Correlation function of dyonic strings, Phys. Rev. D 84 (2011) 026009 [arXiv:1104.1896] [INSPIRE].

    ADS  Google Scholar 

  17. C. Ahn and P. Bozhilov, Three-point correlation functions of giant magnons with finite size, Phys. Lett. B 702 (2011) 286 [arXiv:1105.3084] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  18. D. Arnaudov, R. Rashkov and R. Rashkov, Quadratic corrections to three-point functions, Fortsch. Phys. 60 (2012) 217 [arXiv:1106.0859] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. R.A. Janik and A. Wereszczynski, Correlation functions of three heavy operators: the AdS contribution, JHEP 12 (2011) 095 [arXiv:1109.6262] [INSPIRE].

    Article  ADS  Google Scholar 

  20. J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring three-point functions and integrability II. Weak/strong coupling match, JHEP 09 (2011) 029 [arXiv:1104.5501] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring three-point functions and integrability, JHEP 09 (2011) 028 [arXiv:1012.2475] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. N. Gromov, A. Sever and P. Vieira, Tailoring three-point functions and integrability III. Classical tunneling, JHEP 07 (2012) 044 [arXiv:1111.2349] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. N. Gromov and P. Vieira, Quantum integrability for three-point functions, arXiv:1202.4103 [INSPIRE].

  24. D. Serban, A note on the eigenvectors of long-range spin chains and their scalar products, arXiv:1203.5842 [INSPIRE].

  25. I. Kostov, Classical limit of the three-point function of N = 4 supersymmetric Yang-Mills theory from integrability, Phys. Rev. Lett. 108 (2012) 261604 [arXiv:1203.6180] [INSPIRE].

    Article  ADS  Google Scholar 

  26. G. Grignani and A. Zayakin, Matching three-point functions of BMN operators at weak and strong coupling, JHEP 06 (2012) 142 [arXiv:1204.3096] [INSPIRE].

    Article  ADS  Google Scholar 

  27. K. Okuyama and L.-S. Tseng, Three-point functions in N = 4 SYM theory at one-loop, JHEP 08 (2004) 055 [hep-th/0404190] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. 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].

    Article  MathSciNet  ADS  Google Scholar 

  29. G. Georgiou, V. Gili, A. Grossardt and J. Plefka, Three-point functions in planar N = 4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order, JHEP 04 (2012) 038 [arXiv:1201.0992] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. A. Bissi, T. Harmark and M. Orselli, Holographic 3-point function at one loop, JHEP 02 (2012)133 [arXiv:1112.5075] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. A. Bissi, C. Kristjansen, D. Young and K. Zoubos, Holographic three-point functions of giant gravitons, JHEP 06 (2011) 085 [arXiv:1103.4079] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. O. Foda, N = 4 SYM structure constants as determinants, JHEP 03 (2012) 096 [arXiv:1111.4663] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. S. Frolov and A.A. Tseytlin, Rotating string solutions: AdS/CFT duality in nonsupersymmetric sectors, Phys. Lett. B 570 (2003) 96 [hep-th/0306143] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  34. T. Harmark, K.R. Kristjansson and M. Orselli, Matching gauge theory and string theory in a decoupling limit of AdS/CFT, JHEP 02 (2009) 027 [arXiv:0806.3370] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N =4 super Yang-Mills,JHEP 04(2002)013 [hep-th/0202021][INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. M. Spradlin and A. Volovich, Superstring interactions in a pp wave background. 2, JHEP 01 (2003)036 [hep-th/0206073] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. S. Dobashi, H. Shimada and T. Yoneya, Holographic reformulation of string theory on AdS 5 × S 5 background in the pp wave limit, Nucl. Phys. B 665 (2003) 94 [hep-th/0209251] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. J. Pearson, M. Spradlin, D. Vaman, H.L. Verlinde and A. Volovich, Tracing the string: BMN correspondence at finite J 2 /N , JHEP 05 (2003) 022 [hep-th/0210102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. A. Pankiewicz and B.J. Stefanski, pp wave light cone superstring field theory, Nucl. Phys. B 657 (2003)79 [hep-th/0210246] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. Y.-H. He, J.H. Schwarz, M. Spradlin and A. Volovich, Explicit formulas for Neumann coefficients in the plane wave geometry, Phys. Rev. D 67 (2003) 086005 [hep-th/0211198] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  41. A. Pankiewicz and B.J. Stefanski, On the uniqueness of plane wave string field theory, hep-th/0308062 [INSPIRE].

  42. P. Di Vecchia, J.L. Petersen, M. Petrini, R. Russo and A. Tanzini, The three string vertex and the AdS/CFT duality in the pp wave limit, Class. Quant. Grav. 21 (2004) 2221 [hep-th/0304025] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  43. S. Dobashi and T. Yoneya, Resolving the holography in the plane-wave limit of AdS/CFT correspondence, Nucl. Phys. B 711 (2005) 3 [hep-th/0406225] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. S. Dobashi and T. Yoneya, Impurity non-preserving 3-point correlators of BMN operators from pp-wave holography. I. Bosonic excitations, Nucl. Phys. B 711 (2005) 54 [hep-th/0409058] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. H. Shimada, Holography at string field theory level: conformal three point functions of BMN operators, Phys. Lett. B 647 (2007) 211 [hep-th/0410049] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  46. S. Lee and R. Russo, Holographic cubic vertex in the pp-wave, Nucl. Phys. B 705 (2005) 296 [hep-th/0409261] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. G. Grignani, M. Orselli, B. Ramadanovic, G.W. Semenoff and D. Young, Divergence cancellation and loop corrections in string field theory on a plane wave background, JHEP 12 (2005) 017 [hep-th/0508126] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. G. Grignani, M. Orselli, B. Ramadanovic, G.W. Semenoff and D. Young, AdS/CFT versus string loops, JHEP 06 (2006) 040 [hep-th/0605080] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. C. Kristjansen, J. Plefka, G. Semenoff and M. Staudacher, A new double scaling limit of N =4 super Yang-Mills theory and pp wave strings,Nucl. Phys. B 643(2002)3 [hep-th/0205033] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. N. Beisert, C. Kristjansen, J. Plefka, G. Semenoff and M. Staudacher, BMN correlators and operator mixing in N = 4 super Yang-Mills theory, Nucl. Phys. B 650 (2003) 125 [hep-th/0208178] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. N. Beisert, C. Kristjansen and M. Staudacher, The dilatation operator of conformal N = 4 super Yang-Mills theory, Nucl. Phys. B 664 (2003) 131 [hep-th/0303060] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. G. Georgiou, V.L. Gili and R. Russo, Operator mixing and the AdS/CFT correspondence, JHEP 01 (2009) 082 [arXiv:0810.0499] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  53. G. Georgiou, V.L. Gili and R. Russo, Operator mixing and three-point functions in N = 4 SYM, JHEP 10 (2009) 009 [arXiv:0907.1567] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. J. Minahan and K. Zarembo, The Bethe ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Perugia and INFN — Sezione di Perugia, Via Pascoli, I-06123, Perugia, Italy

    Gianluca Grignani & A. V. Zayakin

  2. Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya ul. 25, 117259, Moscow, Russia

    A. V. Zayakin

Authors
  1. Gianluca Grignani
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  2. A. V. Zayakin
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Correspondence to Gianluca Grignani.

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ArXiv ePrint: 1205.5279

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Grignani, G., Zayakin, A.V. Three-point functions of BMN operators at weak and strong coupling II. One loop matching. J. High Energ. Phys. 2012, 87 (2012). https://doi.org/10.1007/JHEP09(2012)087

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