Skip to main content
SpringerLink
Log in

Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study form factors in \( \mathcal{N}=4 \) SYM at strong coupling in general kinematics and with multi-operator insertions by using gauge/string duality and integrability techniques. This generalizes the AdS3 results of Maldacena and Zhiboedov in two non-trivial aspects. The first generalization to AdS5 space was motivated by its potential connection to strong coupling Higgs-to-three-gluons amplitudes in QCD which was observed recently at weak coupling. The second generalization to multi-operator insertions was motivated as a step towards applying on-shell techniques to compute correlation functions at strong coupling. In this picture, each operator is associated to a monodromy condition on the cusp solutions. We construct Y-systems for both cases. The Y -functions are related to the spacetime (cross) ratios. Their WKB approximations based on a rational function P (z) are also studied. We focus on the short operators, while the prescription is hopefully also applicable for more general operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Z. Bern, L.J. Dixon and D.A. Kosower, N = 4 super-Yang-Mills theory, QCD and collider physics, C. R. Phys. 5 (2004) 955 [hep-th/0410021] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. A.V. Kotikov, L.N. Lipatov, A.I. Onishchenko and V.N. 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].

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

  4. 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].

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

  6. N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. (2007) P01021 [hep-th/0610251] [INSPIRE].

  7. N. Gromov, V. Kazakov and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 103 (2009) 131601 [arXiv:0901.3753] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  9. G. Arutyunov and S. Frolov, Thermodynamic Bethe ansatz for the AdS 5 × S 5 mirror model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. N. Gromov, V. Kazakov, S. Leurent and D. Volin, Solving the AdS/CFT Y-system, JHEP 07 (2012) 023 [arXiv:1110.0562] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. G. Mandal, N.V. Suryanarayana and S.R. Wadia, Aspects of semiclassical strings in AdS 5, Phys. Lett. B 543 (2002) 81 [hep-th/0206103] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  12. J.A. 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 

  13. I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  17. A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes in N = 4 super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [arXiv:0707.1153] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. 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 [arXiv:0712.1223] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. L.J. Mason and D. Skinner, The complete planar S-matrix of N = 4 SYM as a Wilson loop in twistor space, JHEP 12 (2010) 018 [arXiv:1009.2225] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. S. Caron-Huot and S. He, Jumpstarting the all-loop S-matrix of planar N = 4 super Yang-Mills, JHEP 07 (2012) 174 [arXiv:1112.1060] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. L.F. Alday, B. Eden, G.P. Korchemsky, J.M. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, JHEP 09 (2011) 123 [arXiv:1007.3243] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. B. Eden, G.P. Korchemsky and E. Sokatchev, From correlation functions to scattering amplitudes, JHEP 12 (2011) 002 [arXiv:1007.3246] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. L.F. Alday and J.M. Maldacena, Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space, JHEP 11 (2009) 082 [arXiv:0904.0663] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. L.F. Alday, D. Gaiotto and J.M. Maldacena, Thermodynamic bubble ansatz, JHEP 09 (2011) 032 [arXiv:0911.4708] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. L.F. Alday, J.M. Maldacena, A. Sever and P. Vieira, Y-system for scattering amplitudes, J. Phys. A 43 (2010) 485401 [arXiv:1002.2459] [INSPIRE].

    MathSciNet  Google Scholar 

  27. G. Yang, Scattering amplitudes at strong coupling for 4K gluons, JHEP 12 (2010) 082 [arXiv:1004.3983] [INSPIRE].

    Article  ADS  Google Scholar 

  28. G. Yang, A simple collinear limit of scattering amplitudes at strong coupling, JHEP 03 (2011) 087 [arXiv:1006.3306] [INSPIRE].

    Article  ADS  Google Scholar 

  29. J. Bartels, J. Kotanski and V. Schomerus, Excited hexagon Wilson loops for strongly coupled N = 4 SYM, JHEP 01 (2011) 096 [arXiv:1009.3938] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. J. Bartels, V. Schomerus and M. Sprenger, Multi-Regge limit of the n-gluon bubble ansatz, JHEP 11 (2012) 145 [arXiv:1207.4204] [INSPIRE].

    Article  ADS  Google Scholar 

  31. Y. Hatsuda, K. Ito, K. Sakai and Y. Satoh, Six-point gluon scattering amplitudes from Z 4 -symmetric integrable model, JHEP 09 (2010) 064 [arXiv:1005.4487] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. Y. Hatsuda, K. Ito and Y. Satoh, Null-polygonal minimal surfaces in AdS 4 from perturbed W minimal models, JHEP 02 (2013) 067 [arXiv:1211.6225] [INSPIRE].

    Article  ADS  Google Scholar 

  33. V.A. Kazakov, A. Marshakov, J.A. Minahan and K. Zarembo, Classical/quantum integrability in AdS/CFT, JHEP 05 (2004) 024 [hep-th/0402207] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. J. Polchinski and L. Susskind, String theory and the size of hadrons, hep-th/0112204 [INSPIRE].

  36. L.F. Alday and J.M. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. J.M. Maldacena and A. Zhiboedov, Form factors at strong coupling via a Y-system, JHEP 11 (2010) 104 [arXiv:1009.1139] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. W.L. van Neerven, Infrared behavior of on-shell form-factors in a N = 4 supersymmetric Yang-Mills field theory, Z. Phys. C 30 (1986) 595 [INSPIRE].

    ADS  Google Scholar 

  39. 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 [arXiv:1011.1899] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. L.V. Bork, D.I. Kazakov and G.S. Vartanov, On form factors in N = 4 SYM, JHEP 02 (2011) 063 [arXiv:1011.2440] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. A. Brandhuber, O. Gurdogan, R. Mooney, G. Travaglini and G. Yang, Harmony of super form factors, JHEP 10 (2011) 046 [arXiv:1107.5067] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. L.V. Bork, D.I. Kazakov and G.S. Vartanov, On MHV form factors in superspace for \( \mathcal{N}=4 \) SYM theory, JHEP 10 (2011) 133 [arXiv:1107.5551] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. T. Gehrmann, J.M. Henn and T. Huber, The three-loop form factor in N = 4 super Yang-Mills, JHEP 03 (2012) 101 [arXiv:1112.4524] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. A. Brandhuber, G. Travaglini and G. Yang, Analytic two-loop form factors in N = 4 SYM, JHEP 05 (2012) 082 [arXiv:1201.4170] [INSPIRE].

    Article  ADS  Google Scholar 

  45. T. Gehrmann, M. Jaquier, E.W.N. Glover and A. Koukoutsakis, Two-loop QCD corrections to the helicity amplitudes for H → 3 partons, JHEP 02 (2012) 056 [arXiv:1112.3554] [INSPIRE].

    Article  ADS  Google Scholar 

  46. R.H. Boels, B.A. Kniehl, O.V. Tarasov and G. Yang, Color-kinematic duality for form factors, JHEP 02 (2013) 063 [arXiv:1211.7028] [INSPIRE].

    Article  ADS  Google Scholar 

  47. O.T. Engelund and R. Roiban, Correlation functions of local composite operators from generalized unitarity, JHEP 03 (2013) 172 [arXiv:1209.0227] [INSPIRE].

    Article  ADS  Google Scholar 

  48. D.J. Gross and P.F. Mende, String theory beyond the Planck scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. R. Kallosh and A.A. Tseytlin, Simplifying superstring action on AdS 5 × S 5, JHEP 10 (1998) 016 [hep-th/9808088] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. T.H. Buscher, A symmetry of the string background field equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  51. N. Berkovits and J.M. Maldacena, Fermionic T-duality, dual superconformal symmetry and the amplitude/Wilson loop connection, JHEP 09 (2008) 062 [arXiv:0807.3196] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. N. Beisert, R. Ricci, A.A. Tseytlin and M. Wolf, Dual superconformal symmetry from AdS 5 × S 5 superstring integrability, Phys. Rev. D 78 (2008) 126004 [arXiv:0807.3228] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  54. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. L.F. Alday, E.I. Buchbinder and A.A. Tseytlin, Correlation function of null polygonal Wilson loops with local operators, JHEP 09 (2011) 034 [arXiv:1107.5702] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  57. 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 [arXiv:0707.4254] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. C. Anastasiou, Z. Bern, L.J. Dixon and D.A. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett. 91 (2003) 251602 [hep-th/0309040] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [hep-th/0505205] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  60. N. Berkovits, Super Poincaré covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  61. H.J. De Vega and N.G. Sanchez, Exact integrability of strings in D-dimensional de Sitter space-time, Phys. Rev. D 47 (1993) 3394 [INSPIRE].

    ADS  Google Scholar 

  62. A. Jevicki, K. Jin, C. Kalousios and A. Volovich, Generating AdS string solutions, JHEP 03 (2008) 032 [arXiv:0712.1193] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  63. H. Dorn, G. Jorjadze and S. Wuttke, On spacelike and timelike minimal surfaces in AdS n , JHEP 05 (2009) 048 [arXiv:0903.0977] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  64. K. Pohlmeyer, Integrable Hamiltonian systems and interactions through quadratic constraints, Commun. Math. Phys. 46 (1976) 207 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP 05 (2013) 135 [arXiv:0905.1473] [INSPIRE].

    Article  ADS  Google Scholar 

  66. J. Schwarz, Opening lecture, talk given at Strings 2012, München Germany, 23-28 Jul 2012, http://wwwth.mpp.mpg.de/members/strings/strings2012/stringsfiles/program/Talks/Monday/Schwarz.pdf.

  67. C.-N. Yang and C.P. Yang, Thermodynamics of one-dimensional system of bosons with repulsive delta function interaction, J. Math. Phys. 10 (1969) 1115 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  68. A.B. Zamolodchikov, Thermodynamic Bethe ansatz in relativistic models. Scaling three state Potts and Lee-Yang models, Nucl. Phys. B 342 (1990) 695 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  69. L.F. Alday, D. Gaiotto, J.M. Maldacena, A. Sever and P. Vieira, An operator product expansion for polygonal null Wilson loops, JHEP 04 (2011) 088 [arXiv:1006.2788] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  70. D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [INSPIRE].

  71. A.V. Zhiboedov, Form factors in theories with gravity duals, Nucl. Phys. Proc. Suppl. 216 (2011) 276 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  72. A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  73. L.J. Dixon, J.M. Drummond and J.M. Henn, Bootstrapping the three-loop hexagon, JHEP 11 (2011) 023 [arXiv:1108.4461] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  74. J.A. Minahan, Holographic three-point functions for short operators, JHEP 07 (2012) 187 [arXiv:1206.3129] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  76. M. Kruczenski and A.A. Tseytlin, Wilson loops T-dual to short strings, arXiv:1212.4886 [INSPIRE].

  77. 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 

  78. 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].

  79. Y. Kazama and S. Komatsu, Wave functions and correlation functions for GKP strings from integrability, JHEP 09 (2012) 022 [arXiv:1205.6060] [INSPIRE].

    Article  ADS  Google Scholar 

  80. J. Caetano and J. Toledo, χ-systems for correlation functions, arXiv:1208.4548 [INSPIRE].

  81. R.A. Janik and P. Laskos-Grabowski, Surprises in the AdS algebraic curve constructions: Wilson loops and correlation functions, Nucl. Phys. B 861 (2012) 361 [arXiv:1203.4246] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  82. A. Sever, P. Vieira and T. Wang, From polygon Wilson loops to spin chains and back, JHEP 12 (2012) 065 [arXiv:1208.0841] [INSPIRE].

    Article  ADS  Google Scholar 

  83. L. Ferro, T. Lukowski, C. Meneghelli, J. Plefka and M. Staudacher, Harmonic R-matrices for scattering amplitudes and spectral regularization, arXiv:1212.0850 [INSPIRE].

  84. L. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and grassmannians, JHEP 11 (2009) 045 [arXiv:0909.0250] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Zhiquan Gao

  2. Kavli Institute for Theoretical Physics China, Beijing, 100190, China

    Zhiquan Gao

  3. II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761, Hamburg, Germany

    Gang Yang

Authors
  1. Zhiquan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gang Yang.

Additional information

ArXiv ePrint: 1303.2668

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, Z., Yang, G. Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3 . J. High Energ. Phys. 2013, 105 (2013). https://doi.org/10.1007/JHEP06(2013)105

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2013)105

Keywords

Search

Navigation