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Correlation function of null polygonal Wilson loops with local operators

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Abstract

We consider the correlator \( {{{\left\langle {{W_n}\mathcal{O}} \right\rangle }} \left/ {{\left\langle {{W_n}} \right\rangle }} \right.} \) of a light-like polygonal Wilson loop with n cusps with a local operator (like the dilaton or a chiral primary scalar) in planar \( \mathcal{N} = 4 \) super Yang-Mills theory. As a consequence of conformal symmetry, the main part of such correlator is a function F of 3n − 11conformal ratios. The first non-trivial case is n = 4 when F depends on just one conformal ratio ζ. This makes the corresponding correlator one of the simplest non-trivial observables that one would like to compute for generic values of the ‘t Hooft coupling λ. We compute F(ζ, λ) at leading order in both the strong coupling regime (using semiclassical AdS 5 × S 5 string theory) and the weak coupling regime (using perturbative gauge theory). Some results are also obtained for polygonal Wilson loops with more than four edges. Furthermore, we also discuss a connection to the relation between a correlator of local operators at null-separated positions and cusped Wilson loop suggested in ar**v:1007.3243.

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References

  1. N. Beisert et al., Review of AdS/CFT Integrability: An Overview, ar**v:1012.3982 [SPIRES].

  2. D. Serban, Integrability and the AdS/CFT correspondence, J. Phys. A 44 (2011) 124001 [ar**v:1003.4214] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  3. L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [ar**v:0705.0303] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  4. G.P. Korchemsky, J.M. Drummond and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [ar**v:0707.0243] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  5. A. Brandhuber, P. Heslop and G. Travaglini, MHV Amplitudes in N = 4 Super Yang-Mills and Wilson Loops, Nucl. Phys. B 794 (2008) 231 [ar**v:0707.1153] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  6. L.F. Alday and R. Roiban, Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence, Phys. Rept. 468 (2008) 153 [ar**v:0807.1889] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  7. J.M. Henn, Duality between Wilson loops and gluon amplitudes, Fortsch. Phys. 57 (2009) 729 [ar**v:0903.0522] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. I.A. Korchemskaya and G.P. Korchemsky, On lightlike Wilson loops, Phys. Lett. B 287 (1992) 169 [SPIRES].

    ADS  Google Scholar 

  9. A. Bassetto, I.A. Korchemskaya, G.P. Korchemsky and G. Nardelli, Gauge invariance and anomalous dimensions of a light cone Wilson loop in lightlike axial gauge, Nucl. Phys. B 408 (1993) 62 [hep-ph/9303314] [SPIRES].

    Article  ADS  Google Scholar 

  10. M. Kruczenski, A note on twist two operators in N = 4 SYM and Wilson loops in Minkowski signature, JHEP 12 (2002) 024 [hep-th/0210115] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  11. Y. Makeenko, Light-cone Wilson loops and the string/gauge correspondence, JHEP 01 (2003) 007 [hep-th/0210256] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  12. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys. B 826 (2010) 337 [ar**v:0712.1223] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  13. A.M. Polyakov, Gauge Fields as Rings of Glue, Nucl. Phys. B 164 (1980) 171 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  14. G.P. Korchemsky and A.V. Radyushkin, Loop space formalism and renormalization group for the infrared asymptotics of QCD, Phys. Lett. B 171 (1986) 459 [SPIRES].

    ADS  Google Scholar 

  15. G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson Loops Beyond the Leading Order, Nucl. Phys. B 283 (1987) 342 [SPIRES].

    Article  ADS  Google Scholar 

  16. G.P. Korchemsky and G. Marchesini, Structure function for large x and renormalization of Wilson loop, Nucl. Phys. B 406 (1993) 225 [hep-ph/9210281] [SPIRES].

    Article  ADS  Google Scholar 

  17. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys. B 815 (2009) 142 [ar**v:0803.1466] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  18. C. Anastasiou et al., T wo-Loop Polygon Wilson Loops in N = 4 SYM, JHEP 05 (2009) 115 [ar**v:0902.2245] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  19. V. Del Duca, C. Duhr and V.A. Smirnov, The Two-Loop Hexagon Wilson Loop in N = 4 SYM, JHEP 05 (2010) 084 [ar**v:1003.1702] [SPIRES].

    Article  ADS  Google Scholar 

  20. A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical Polylogarithms for Amplitudes and Wilson Loops, Phys. Rev. Lett. 105 (2010) 151605 [ar**v:1006.5703] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  21. L.F. Alday, D. Gaiotto and J. Maldacena, Thermodynamic Bubble Ansatz, ar**v:0911.4708 [SPIRES].

  22. D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, Pulling the straps of polygons, ar**v:1102.0062 [SPIRES].

  23. L.F. Alday, J. Maldacena, A. Sever and P. Vieira, Y-system for Scattering Amplitudes, J. Phys. A 43 (2010) 485401 [ar**v:1002.2459] [SPIRES].

    MathSciNet  Google Scholar 

  24. L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, ar**v:1007.3243 [SPIRES].

  25. 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 

  26. K. Zarembo, Open string fluctuations in AdS 5 × S 5 and operators with large R charge, Phys. Rev. D 66 (2002) 105021 [hep-th/0209095] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  27. V. Pestun and K. Zarembo, Comparing strings in AdS 5 × S 5 to planar diagrams: An example, Phys. Rev. D 67 (2003) 086007 [hep-th/0212296] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  28. J. Gomis, S. Matsuura, T. Okuda and D. Trancanelli, Wilson loop correlators at strong coupling: from matrices to bubbling geometries, JHEP 08 (2008) 068 [ar**v:0807.3330] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

  30. A. Miwa and T. Yoneya, Holography of Wilson-loop expectation values with local operator insertions, JHEP 12 (2006) 060 [hep-th/0609007] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  31. M. Sakaguchi and K. Yoshida, A Semiclassical String Description of Wilson Loop with Local Operators, Nucl. Phys. B 798 (2008) 72 [ar**v:0709.4187] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  32. A. Miwa, BMN operators from Wilson loop, JHEP 06 (2005) 050 [hep-th/0504039] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  33. G.W. Semenoff and D. Young, Exact 1/4 BPS loop: Chiral primary correlator, Phys. Lett. B 643 (2006) 195 [hep-th/0609158] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  34. L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [ar**v:0710.1060] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  35. J. Maldacena and A. Zhiboedov, Form factors at strong coupling via a Y-system, JHEP 11 (2010) 104 [ar**v:1009.1139] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  36. A. Brandhuber, B. Spence, G. Travaglini and G. Yang, Form Factors in N = 4 Super Yang-Mills and Periodic Wilson Loops, JHEP 01 (2011) 134 [ar**v:1011.1899] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  37. L.V. Bork, D.I. Kazakov and G.S. Vartanov, On form factors in N = 4 SYM, JHEP 02 (2011) 063 [ar**v:1011.2440] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  38. M. Kruczenski, R. Roiban, A. Tirziu and A.A. Tseytlin, Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS 5 × S 5, Nucl. Phys. B 791 (2008) 93 [ar**v:0707.4254] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  39. S. Ryang, Conformal SO(2, 4) Transformations of the One-Cusp Wilson Loop Surface, Phys. Lett. B 659 (2008) 894 [ar**v:0710.1673] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  40. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A semi-classical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  41. S. Frolov and A.A. Tseytlin, Semiclassical quantization of rotating superstring in AdS 5 × S 5, JHEP 06 (2002) 007 [hep-th/0204226] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  42. S. Frolov, A. Tirziu and A.A. Tseytlin, Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT, Nucl. Phys. B 766 (2007) 232 [hep-th/0611269] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  44. 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 [ar**v:1008.4921] [SPIRES].

    ADS  Google Scholar 

  45. K. Zarembo, Holographic three-point functions of semiclassical states, JHEP 09 (2010) 030 [ar**v:1008.1059] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  46. 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 [ar**v:1008.1070] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  47. L.F. Alday and J. Maldacena, Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space, JHEP 11 (2009) 082 [ar**v:0904.0663] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  48. L.F. Alday and J. Maldacena, Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling, ar**v:0903.4707 [SPIRES].

  49. K. Symanzik, On Calculations in conformal invariant field theories, Lett. Nuovo Cim. 3 (1972) 734 [SPIRES].

    Article  Google Scholar 

  50. M.A. Shifman, Wilson Loop in Vacuum Fields, Nucl. Phys. B 173 (1980) 13 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  52. A.M. Polyakov, Gauge fields and space-time, Int. J. Mod. Phys. A 17S1 (2002) 119 [hep-th/0110196] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  53. A.A. Tseytlin, On semiclassical approximation and spinning string vertex operators in AdS 5 × S 5, Nucl. Phys. B 664 (2003) 247 [hep-th/0304139] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  54. L.F. Alday and J.M. Maldacena, Comments on operators with large spin, JHEP 11 (2007) 019 [ar**v:0708.0672] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  55. E.I. Buchbinder, Infrared Limit of Gluon Amplitudes at Strong Coupling, Phys. Lett. B 654 (2007) 46 [ar**v:0706.2015] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  56. E.I. Buchbinder, Energy-Spin Trajectories in AdS 5 × S 5 from Semiclassical Vertex Operators, JHEP 04 (2010) 107 [ar**v:1002.1716] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  57. L.F. Alday, Review of AdS/CFT Integrability, Chapter V.3: Scattering Amplitudes at Strong Coupling, ar**v:1012.4003 [SPIRES].

  58. D. Gaiotto, G.W. Moore and A. Neitzke, Wall-Crossing in Coupled 2 d-4d Systems, ar**v:1103.2598 [SPIRES].

  59. J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  60. S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  61. L. Andrianopoli and S. Ferrara, K-K excitations on AdS 5 × S 5 as N = 4 *primary* superfields, Phys. Lett. B 430 (1998) 248 [hep-th/9803171] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  62. S. Ferrara, M.A. Lledó and A. Zaffaroni, Born-Infeld corrections to D3 brane action in AdS 5 × S 5 and N = 4, D = 4 primary superfields, Phys. Rev. D 58 (1998) 105029 [hep-th/9805082] [SPIRES].

    ADS  Google Scholar 

  63. I.R. Klebanov, W. Taylor and M. Van Raamsdonk, Absorption of dilaton partial waves by D 3-branes, Nucl. Phys. B 560 (1999) 207 [hep-th/9905174] [SPIRES].

    Article  ADS  Google Scholar 

  64. H. Liu and A.A. Tseytlin, Dilaton-fixed scalar correlators and AdS 5 × S 5 — SYM correspondence, JHEP 10 (1999) 003 [hep-th/9906151] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  65. B.M. McCoy, C.A. Tracy and T.T. Wu, Painleve Functions of the Third Kind, J. Math. Phys. 18 (1977) 1058 [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, OX1 3LB, U.K.

    L. F. Alday

  2. The Blackett Laboratory, Imperial College, London, SW7 2AZ, U.K.

    E. I. Buchbinder & A.A. Tseytlin

  3. Lebedev Institute, Moscow, Russia

    A.A. Tseytlin

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  1. L. F. Alday
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  2. E. I. Buchbinder
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  3. A.A. Tseytlin
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Alday, L.F., Buchbinder, E.I. & Tseytlin, A. Correlation function of null polygonal Wilson loops with local operators. J. High Energ. Phys. 2011, 34 (2011). https://doi.org/10.1007/JHEP09(2011)034

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