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More three-point correlators of giant magnons with finite size

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Abstract

In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to heavy string states, while the third vertex corresponds to a light state. This is done for the case when the heavy string states are finite-size giant magnons with one or two angular momenta, and for two different choices of the light state, corresponding to dilaton operator and primary scalar operator. The relevant operators in the dual gauge theory are \( Tr\left( {F_{\mu \nu }^2{Z^j} + \ldots } \right) \) and Tr(Z j). We first consider the case of AdS 5 × S 5 and \( \mathcal{N} = 4 \) super Yang-Mills. Then we extend the obtained results to the γ-deformed AdS 5 × S γ 5, dual to \( \mathcal{N} = 1 \) super Yang-Mills theory, arising as an exactly marginal deformation of \( \mathcal{N} = 4 \) super Yang-Mills.

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References

  1. A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241 (1984) 333.

    Article  ADS  MathSciNet  Google Scholar 

  2. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  5. N. Beisert et al., Review of AdS/CFT integrability: an overview, arXiv:1012.3982 [SPIRES].

  6. O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  7. S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [SPIRES].

    Article  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] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  9. G. Chalmers, H. Nastase, K. Schalm and R. Siebelink, R-current correlators in N = 4 super Yang-Mills theory from Anti-de Sitter supergravity, Nucl. Phys. B 540 (1999) 247 [hep-th/9805105] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  10. 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] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  11. G. Arutyunov and S. Frolov, Some cubic couplings in type IIB supergravity on AdS 5 × S 5 and three-point functions in SYM(4) at large-N, Phys. Rev. D 61 (2000) 064009 [hep-th/9907085] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  12. R.A. Janik, P. Surowka and A. Wereszczynski, On correlation functions of operators dual to classical spinning string states, JHEP 05 (2010) 030 [arXiv:1002.4613] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  16. R. Roiban and A.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] [SPIRES].

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  18. S. Ryang, Correlators of vertex operators for circular strings with winding numbers in AdS 5 × S 5, JHEP 01 (2011) 092 [arXiv:1011.3573] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  22. E.I. Buchbinder and A.A. Tseytlin, Semiclassical four-point functions in AdS 5 × S 5, JHEP 02 (2011) 072 [arXiv:1012.3740] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. D. Arnaudov, R.C. 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] [SPIRES].

    ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  28. L.F. Alday and A.A. Tseytlin, On strong-coupling correlation functions of circular Wilson loops and local operators, arXiv:1105.1537 [SPIRES].

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

    ADS  MathSciNet  Google Scholar 

  30. B.-H. Lee and C. Park, Finite size effect on the magnon’s correlation functions, arXiv:1105.3279 [SPIRES].

  31. T. Klose and T. McLoughlin, A light-cone approach to three-point functions in AdS 5 × S 5, arXiv:1106.0495 [SPIRES].

  32. D. Arnaudov and R.C. Rashkov, Three-point correlators: examples from Lunin-Maldacena background, arXiv:1106.4298 [SPIRES].

  33. C. Ahn and P. Bozhilov, Three-point correlation function of giant magnons in the Lunin-Maldacena background, arXiv:1106.5656 [SPIRES].

  34. G. Georgiou, SL(2) sector: weak/strong coupling agreement of three-point correlators, arXiv:1107.1850 [SPIRES].

  35. M. Kruczenski, J. Russo and A.A. Tseytlin, Spiky strings and giant magnons on S 5, JHEP 10 (2006) 002 [hep-th/0607044] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  36. L.F. Alday, G. Arutyunov and S. Frolov, Green-Schwarz strings in TsT-transformed backgrounds, JHEP 06 (2006) 018 [hep-th/0512253] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  37. Y. Hatsuda and R. Suzuki, Finite-size effects for dyonic giant magnons, Nucl. Phys. B 800 (2008) 349 [arXiv:0801.0747] [SPIRES].

    Article  ADS  Google Scholar 

  38. D.V. Bykov and S. Frolov, Giant magnons in TsT-transformed AdS 5 × S 5, JHEP 07 (2008) 071 [arXiv:0805.1070] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  39. C. Ahn and P. Bozhilov, Finite-size dyonic giant magnons in TsT-transformed AdS 5 × S 5, JHEP 07 (2010) 048 [arXiv:1005.2508] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  40. D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large-N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  41. P. Bozhilov, Close to the giant magnons, arXiv:1010.5465 [SPIRES].

  42. R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  43. A.P. Prudnikov, Yu.A. Brychkov and O.I. Marichev, Integrals and series. Volume 3: more special functions, Gordon and Breach, U.S.A. (1990).

    MATH  Google Scholar 

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  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria

    Plamen Bozhilov

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  1. Plamen Bozhilov
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ArXiv ePrint: 1107.2645

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Bozhilov, P. More three-point correlators of giant magnons with finite size. J. High Energ. Phys. 2011, 121 (2011). https://doi.org/10.1007/JHEP08(2011)121

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