Skip to main content
Log in

Review of AdS/CFT Integrability, Chapter V.3: Scattering Amplitudes at Strong Coupling

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We review the computation of scattering amplitudes of planar maximally super-symmetric Yang–Mills at strong coupling. By using the AdS/CFT duality the problem boils down to the computation of the area of certain minimal surfaces on AdS. The integrability of the model can then be efficiently used in order to give an answer for the problem in terms of a set of integral equations.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Roiban, R.: Review of AdS/CFT Integrability, Chapter V.1: Scattering amplitudes—a brief introduction. Lett. Math. Phys. Published in this volume. arXiv:1012.4001 [hep-th]

  2. Drummond, J.: Review of AdS/CFT Integrability, Chapter V.2: Dual superconformal symmetry. Lett. Math. Phys. Published in this volume. arXiv:1012.4002 [hep-th]

  3. Maldacena J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys 2, 231 (1998)

    MathSciNet  ADS  MATH  Google Scholar 

  4. Maldacena J.M: The large N limit of superconformal field theories and supergravity. Int. J. Theor. Phys 38, 1113, (1999).arXiv:hep-th/9711200

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Maldacena, J.M.: Wilson loops in large N field theories. Phys. Rev. Lett. 80, 4859 (1998). arXiv:hep-th/9803002

    Google Scholar 

  7. Alday L.F., Maldacena J.M.: Gluon scattering amplitudes at strong coupling. JHEP 0706, 064 (2007) arXiv:0705.0303[hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  8. Alday L.F., Henn J.M., Plefka J., Schuster T.: Scattering into the fifth dimension of N = 4 super Yang–Mills. JHEP 1001, 077 (2010) arXiv:0908.0684 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  9. Gross D.J., Mende P.F.: String theory beyond the planck scale. Nucl. Phys. B303, 407 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  10. McGreevy J., Sever A.: Planar scattering amplitudes from Wilson loops. JHEP 0808, 078 (2008) arXiv:0806.0668 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  11. Ito K., Nastase H., Iwasaki K.: Gluon scattering in N = 4 super Yang–Mills at finite temperature. Prog. Theor. Phys 120, 99 (2008) arXiv:0711.3532 [hep-th]

    Article  ADS  MATH  Google Scholar 

  12. Georgiou, G., Giataganas, D.: Gluon scattering amplitudes in finite temperature gauge/ gravity dualities. arXiv:1011.6339 [hep-th]

  13. Dorn H., Drukker N., Jorjadze G., Kalousios C.: Space-like minimal surfaces in AdS ×  S. JHEP 1004, 004 (2010) arXiv:0912.3829 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  14. McGreevy J., Sever A.: Quark scattering amplitudes at strong coupling. JHEP 0802, 015 (2008) arXiv:0710.0393 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  15. Komargodski Z., Razamat S.S.: Planar quark scattering at strong coupling and universality. JHEP 0801, 044 (2008) arXiv:0707.4367 [hep-th]

    Article  ADS  Google Scholar 

  16. Barnes E., Vaman D.: Massive quark scattering at strong coupling from AdS/CFT. Phys. Rev. D 81, 126007 (2010) arXiv:0911.0010 [hep-th]

    Article  ADS  Google Scholar 

  17. Kruczenski M.: A note on twist two operators in N = 4 SYM and Wilson loops in Minkowski signature. JHEP 0212, 024 (2002) arXiv:hep-th/0210115

    Article  MathSciNet  ADS  Google Scholar 

  18. Gubser S.S., Klebanov I.R., Polyakov A.M.: A semi-classical limit of the gauge/string correspondence. Nucl. Phys. B 636, 99 (2002) arXiv:hep-th/0204051

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  20. Drummond J.M., Henn J., Smirnov V.A., Sokatchev E.: Magic identities for conformal four-point integrals. JHEP 0701, 064 (2007) arXiv:hep-th/0607160

    Article  MathSciNet  ADS  Google Scholar 

  21. Komargodski Z.: On collinear factorization of Wilson loops and MHV amplitudes in N = 4 SYM. JHEP 0805, 019 (2008) arXiv:0801.3274 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  22. Alday L.F.: Lectures on scattering amplitudes via AdS/CFT. Fortsch. Phys 56, 816 (2008) arXiv:0804.0951 [hep-th]

    Article  MathSciNet  MATH  ADS  Google Scholar 

  23. Alday L.F., Maldacena J.: Comments on gluon scattering amplitudes via AdS/CFT. JHEP 0711, 068 (2007) arXiv:0710.1060 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  24. Bern, Z., Dixon, L.J., Kosower, D.A., Roiban, R., Spradlin, M., Vergu, C., Volovich, A.: The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang–Mills theory. Phys. Rev. D 78, 045007 (2008). arXiv:0803.1465 [hep-th]

    Google Scholar 

  25. Buscher T.H.: Path integral derivation of quantum duality in nonlinear sigma models. Phys. Lett. B201, 466 (1988)

    MathSciNet  ADS  Google Scholar 

  26. Berkovits N., Maldacena J.: Fermionic T-duality, dual superconformal symmetry, and the amplitude/wilson loop connection. JHEP 0809, 062 (2008) arXiv:0807.3196 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  27. Beisert N., Ricci R., Tseytlin A.A., Wolf M.: Dual superconformal symmetry from AdS5 × S5 superstring integrability. Phys. Rev. D 78, 126004 (2008) arXiv:0807.3228 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  28. Alday, L.F., Maldacena, J.: Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling. arXiv:0903.4707 [hep-th]

  29. Alday L.F., Maldacena J.: Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space. JHEP 0911, 082 (2009) arXiv:0904.0663 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  30. Alday, L.F., Gaiotto, D., Maldacena, J.: Thermodynamic bubble ansatz. arXiv:0911. 4708 [hep-th]

  31. Alday, L.F., Maldacena, J., Sever, A., Vieira, P.: Y-system for scattering amplitudes. arXiv:1002.2459 [hep-th]

  32. Burrington B.A., Gao P.: Minimal surfaces in AdS space and integrable systems. JHEP 1004, 060 (2010) arXiv:0911.4551[hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  33. Hatsuda Y., Ito K., Sakai K., Satoh Y.: Thermodynamic Bethe ansatz equations for minimal surfaces in AdS(3). JHEP 1004, 108 (2010) arXiv:1002.2941 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  34. Gaiotto D., Moore G.W., Neitzke A.: Four-dimensional wall-crossing via three-dimensional field theory. Commun. Math. Phys 299, 163 (2010) arXiv:0807.4723 [hep-th]

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

  36. De Vega H.J., Sanchez N.G.: Exact integrability of strings in D-dimensional de Sitter space–time. Phys. Rev. D47, 3394 (1993)

    MathSciNet  ADS  Google Scholar 

  37. Jevicki, A., Jin, K., Kalousios, C., Volovich, A.: Generating AdS string solutions. JHEP 0803, 032 (2008). arXiv:0712.1193 [hep-th]

  38. Dorn H.: Some comments on spacelike minimal surfaces with null polygonal boundaries in AdS m . JHEP 1002, 013 (2010) arXiv:0910.0934 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  39. Zamolodchikov A.B.: Thermodynamic Bethe ansatz in relativistic models scaling three state Potts and Lee-Yang models. Nucl. Phys. B342, 695 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  40. Bena I., Polchinski J., Roiban R.: Hidden symmetries of the AdS(5) × S**5 superstring. Phys. Rev. D 69, 046002 (2004) arXiv:hep-th/0305116

    Article  MathSciNet  ADS  Google Scholar 

  41. Schafer-Nameki, S.: Review of AdS/CFT Integrability, Chapter II.4: The spectral curve. Lett. Math. Phys. Published in this volume. arXiv:1012.3989 [hep-th]

  42. Hatsuda Y., Ito K., Sakai K., Satoh Y.: Six-point gluon scattering amplitudes from Z4-symmetric integrable model. JHEP 1009, 064 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  43. Hatsuda, Y., Ito, K., Sakai, K., Satoh, Y.: g-functions and gluon scattering amplitudes at strong coupling. arXiv:1102.2477 [hep-th]

  44. Bartels J., Kotanski J., Schomerus V.: Excited hexagon Wilson loops for strongly coupled N = 4 SYM. JHEP 1101, 096 (2011) arXiv:1009.3938 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  45. Alday, L.F., Gaiotto, D., Maldacena, J., Sever, A., Vieira, P.: An operator product expansion for polygonal null Wilson loops. arXiv:1006.2788 [hep-th]

  46. Basso, B.: Exciting the GKP string at any coupling. arXiv:1010.5237 [hep-th]

  47. Maldacena J., Zhiboedov A.: Form factors at strong coupling via a Y-system. JHEP 1011, 104 (2010) arXiv:1009.1139 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  48. Brandhuber A., Spence B., Travaglini G., Yang G.: Form factors in N = 4 super Yang–Mills and periodic Wilson loops. JHEP 1101, 134 (2011) arXiv:1011.1899 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luis F. Alday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alday, L.F. Review of AdS/CFT Integrability, Chapter V.3: Scattering Amplitudes at Strong Coupling. Lett Math Phys 99, 507–528 (2012). https://doi.org/10.1007/s11005-011-0518-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-011-0518-5

Mathematics Subject Classification (2010)

Keywords

Navigation