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Annual Review of Nuclear and Particle Science

Volume 71, 2021

What Can We Learn About QCD and Collider Physics from =4 Super Yang–Mills?

Abstract

Tremendous ongoing theory efforts are dedicated to developing new methods for quantum chromodynamics (QCD) calculations. Qualitative rather than incremental advances are needed to fully exploit data that are still to be collected at the LHC. The maximally supersymmetric Yang–Mills theory, super Yang–Mills (sYM), shares with QCD the gluon sector, which contains the most complicated Feynman graphs but also has many special properties and is believed to be solvable exactly. It is natural to ask what we can learn from advances in sYM for addressing difficult problems in QCD. With this in mind, I review several remarkable developments and highlights of recent results in sYM. This includes all-order results for certain scattering amplitudes, novel symmetries, surprising geometrical structures of loop integrands, novel tools for the calculation of Feynman integrals, and bootstrap methods. While several insights and tools have already been carried over to QCD and have contributed to state-of-the-art calculations for LHC physics, I argue that there is a host of further fascinating ideas waiting to be explored.

Keyword(s): anomalous dimensions, Feynman integrals, N=4 super Yang–Mills theory, QCD, scattering amplitudes
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2021-09-21
2025-02-18
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Literature Cited

  1. 1. 
    Shifman M. Eur. Phys. J. C 59:197 2009.
     [Google Scholar]
  2. 2. 
    Sohnius M. Phys. Rep. 128:39 1985.
     [Google Scholar]
  3. 3. 
    Mandelstam S. Nucl. Phys. B 213:149 1983.
     [Google Scholar]
  4. 4. 
    Howe PS, Stelle K, West PC. Phys. Lett. B 124:55 1983.
     [Google Scholar]
  5. 5. 
    Maldacena JM. Int. J. Theor. Phys. 38:1113 1999.
     [Google Scholar]
  6. 6. 
    Gubser S, Klebanov IR, Polyakov AM. Phys. Lett. B 428:105 1998.
     [Google Scholar]
  7. 7. 
    Witten E. Adv. Theor. Math. Phys. 2:253 1998.
     [Google Scholar]
  8. 8. 
    Di Francesco P, Mathieu P, Senechal D Graduate Texts in Contemporary Physics New York: Springer-Verlag 1997.
     [Google Scholar]
  9. 9. 
    Polyakov AM. Nucl. Phys. B 164:171 1980.
     [Google Scholar]
  10. 10. 
    Korchemskaya I, Korchemsky G. Phys. Lett. B 287:169 1992.
     [Google Scholar]
  11. 11. 
    Collins JC, Soper DE, Sterman GF arXiv:hep-ph/0409313 1989.
     [Google Scholar]
  12. 12. 
    Korchemsky G, Marchesini G. Phys. Lett. B 313:433 1993.
     [Google Scholar]
  13. 13. 
    Korchemskaya I, Korchemsky G. Phys. Lett. B 387:346 1996.
     [Google Scholar]
  14. 14. 
    ’t Hooft G. Nucl. Phys. B 72:461 1974.
     [Google Scholar]
  15. 15. 
    Bern Z, Dixon LJ, Smirnov VA. Phys. Rev. D 72:085001 2005.
     [Google Scholar]
  16. 16. 
    Kotikov A, Lipatov L. Nucl. Phys. B 661:19 2003.
     [Google Scholar]
  17. 17. 
    Kotikov AV, Lipatov LN, Onishchenko AI, Velizhanin VN. Phys. Lett. B 595:521 2004.
     [Google Scholar]
  18. 18. 
    Bena I, Polchinski J, Roiban R. Phys. Rev. D 69:046002 2004.
     [Google Scholar]
  19. 19. 
    Dolan L, Nappi CR, Witten E. J. High Energy Phys. 0310:017 2003.
     [Google Scholar]
  20. 20. 
    Belitsky A, Braun V, Gorsky A, Korchemsky G. Int. J. Mod. Phys. A 19:4715 2004.
     [Google Scholar]
  21. 21. 
    Minahan J, Zarembo K. J. High Energy Phys. 0303:013 2003.
     [Google Scholar]
  22. 22. 
    Beisert N, Eden B, Staudacher M. J. Stat. Mech. 0701:P01021 2007.Exact integral equation for the cusp anomalous dimension.
     [Google Scholar]
  23. 23. 
    Bern Z et al. Phys. Rev. D 75:085010 2007.
     [Google Scholar]
  24. 24. 
    Benna M, Benvenuti S, Klebanov I, Scardicchio A. Phys. Rev. Lett. 98:131603 2007.
     [Google Scholar]
  25. 25. 
    Basso B, Korchemsky G, Kotanski J. Phys. Rev. Lett. 100:091601 2008.
     [Google Scholar]
  26. 26. 
    Kruczenski M. J. High Energy Phys. 0212:024 2002.
     [Google Scholar]
  27. 27. 
    Roiban R, Tseytlin AA. J. High Energy Phys. 0711:016 2007.
     [Google Scholar]
  28. 28. 
    Basso B, Korchemsky G. J. Phys. A 42:254005 2009.
     [Google Scholar]
  29. 29. 
    Bianchi L et al. J. High Energy Phys. 1607:14 2016.
     [Google Scholar]
  30. 30. 
    Henn JM, Korchemsky GP, Mistlberger B. J. High Energy Phys. 2004:18 2020.
     [Google Scholar]
  31. 31. 
    Huber T et al. Phys. Lett. B 807:135543 2020.
     [Google Scholar]
  32. 32. 
    von Manteuffel A, Panzer E, Schabinger RM. Phys. Rev. Lett. 124:162001 2020.
     [Google Scholar]
  33. 33. 
    Dixon LJ. J. High Energy Phys. 1801:75 2018.
     [Google Scholar]
  34. 34. 
    Dixon LJ, Magnea L, Sterman GF. J. High Energy Phys. 0808:022 2008.
     [Google Scholar]
  35. 35. 
    Almelid O, Duhr C, Gardi E. Phys. Rev. Lett. 117:172002 2016.
     [Google Scholar]
  36. 36. 
    Anastasiou C, Bern Z, Dixon LJ, Kosower D. Phys. Rev. Lett. 91:251602 2003.
     [Google Scholar]
  37. 37. 
    Alday LF, Maldacena JM. J. High Energy Phys. 0706:064 2007.Prescription for computing scattering amplitudes at strong coupling.
     [Google Scholar]
  38. 38. 
    Drummond J, Korchemsky G, Sokatchev E. Nucl. Phys. B 795:385 2008.
     [Google Scholar]
  39. 39. 
    Brandhuber A, Heslop P, Travaglini G. Nucl. Phys. B 794:231 2008.
     [Google Scholar]
  40. 40. 
    Caron-Huot S. J. High Energy Phys. 1107:58 2011.
     [Google Scholar]
  41. 41. 
    Drummond J, Henn J, Korchemsky G, Sokatchev E. Nucl. Phys. B 815:142 2009.
     [Google Scholar]
  42. 42. 
    Bern Z et al. Phys. Rev. D 78:045007 2008.
     [Google Scholar]
  43. 43. 
    Berkovits N, Maldacena J. J. High Energy Phys. 0809:062 2008.
     [Google Scholar]
  44. 44. 
    Alday LF, Roiban R. Phys. Rep. 468:153 2008.
     [Google Scholar]
  45. 45. 
    Grozin A Springer Tracts in Modern Physics 201 Heavy Quark Effective Theory Berlin: Springer 2004.
     [Google Scholar]
  46. 46. 
    Bauer CW, Fleming S, Pirjol D, Stewart IW. Phys. Rev. D 63:114020 2001.
     [Google Scholar]
  47. 47. 
    Gatheral J. Phys. Lett. B 133:90 1983.
     [Google Scholar]
  48. 48. 
    Alday LF et al. J. High Energy Phys. 1104:88 2011.Near-collinear expansion of Wilson loops from operator product expansion.
     [Google Scholar]
  49. 49. 
    Basso B, Sever A, Vieira P. Phys. Rev. Lett. 111:091602 2013.
     [Google Scholar]
  50. 50. 
    Basso B et al. J. High Energy Phys. 1508:18 2015.
     [Google Scholar]
  51. 51. 
    Bonini A, Fioravanti D, Piscaglia S, Rossi M. J. High Energy Phys. 1604:29 2016.
     [Google Scholar]
  52. 52. 
    Anastasiou C et al. J. High Energy Phys. 0905:115 2009.
     [Google Scholar]
  53. 53. 
    Arkani-Hamed N, Bourjaily JL, Cachazo F, Trnka J. J. High Energy Phys. 1206:125 2012.
     [Google Scholar]
  54. 54. 
    Henn J, Herrmann E, Parra-Martinez J. J. High Energy Phys. 1810:59 2018.
     [Google Scholar]
  55. 55. 
    Bourjaily JL, Volk M, Von Hippel M. J. High Energy Phys. 2002:95 2020.
     [Google Scholar]
  56. 56. 
    Dixon LJ, Drummond JM, Henn JM. J. High Energy Phys. 1201:24 2012.
     [Google Scholar]
  57. 57. 
    Drummond J, Henn J, Smirnov V, Sokatchev E. J. High Energy Phys. 0701:064 2007.
     [Google Scholar]
  58. 58. 
    Drummond J, Henn J, Korchemsky G, Sokatchev E. Nucl. Phys. B 826:337 2010.
     [Google Scholar]
  59. 59. 
    Drummond JM, Henn J, Korchemsky GP, Sokatchev E. Nucl. Phys. B 828:317 2010.
     [Google Scholar]
  60. 60. 
    Drummond JM, Henn JM, Plefka J. J. High Energy Phys. 0905:046 2009.Yangian symmetry of scattering amplitudes in super Yang–Mills.
     [Google Scholar]
  61. 61. 
    Caron-Huot S, He S. J. High Energy Phys. 1207:174 2012.
     [Google Scholar]
  62. 62. 
    Alday LF, Henn JM, Plefka J, Schuster T. J. High Energy Phys. 1001:77 2010.
     [Google Scholar]
  63. 63. 
    Caron-Huot S, Henn JM. Phys. Rev. Lett. 113:161601 2014.
     [Google Scholar]
  64. 64. 
    Pauli W. Z. Phys. 36:336 1926.
     [Google Scholar]
  65. 65. 
    Ben-Israel R, Tumanov AG, Sever A. J. High Energy Phys. 1808:122 2018.
     [Google Scholar]
  66. 66. 
    Bern Z, Enciso M, Shen CH, Zeng M. Phys. Rev. Lett. 121:121603 2018.
     [Google Scholar]
  67. 67. 
    Henn JM, Mistlberger B. Phys. Rev. Lett. 117:171601 2016.
     [Google Scholar]
  68. 68. 
    Abreu S et al. Phys. Rev. Lett. 122:121603 2019.
     [Google Scholar]
  69. 69. 
    Chicherin D et al. Phys. Rev. Lett. 122:121602 2019.
     [Google Scholar]
  70. 70. 
    Bartels J, Lipatov L, Sabio Vera A. Phys. Rev. D 80:045002 2009.
     [Google Scholar]
  71. 71. 
    Lipatov L. JETP Lett. 59:596 1994.
     [Google Scholar]
  72. 72. 
    Faddeev L, Korchemsky G. Phys. Lett. B 342:311 1995.
     [Google Scholar]
  73. 73. 
    Britto R, Cachazo F, Feng B, Witten E. Phys. Rev. Lett. 94:181602 2005.
     [Google Scholar]
  74. 74. 
    Brandhuber A, Heslop P, Travaglini G. Phys. Rev. D 78:125005 2008.
     [Google Scholar]
  75. 75. 
    Drummond J, Henn J. J. High Energy Phys. 0904:018 2009.
     [Google Scholar]
  76. 76. 
    Dixon LJ, Henn JM, Plefka J, Schuster T. J. High Energy Phys. 1101:35 2011.
     [Google Scholar]
  77. 77. 
    Witten E. Commun. Math. Phys. 252:189 2004.
     [Google Scholar]
  78. 78. 
    Hodges A. J. High Energy Phys. 1305:135 2013.
     [Google Scholar]
  79. 79. 
    Mason L, Skinner D. J. High Energy Phys. 0911:045 2009.
     [Google Scholar]
  80. 80. 
    Carrasco JJM, Johansson H. J. Phys. A 44:454004 2011.
     [Google Scholar]
  81. 81. 
    Ossola G, Papadopoulos CG, Pittau R. Nucl. Phys. B 763:147 2007.
     [Google Scholar]
  82. 82. 
    Berger C et al. Phys. Rev. D 78:036003 2008.
     [Google Scholar]
  83. 83. 
    Badger S, Frellesvig H, Zhang Y. J. High Energy Phys. 1312:45 2013.
     [Google Scholar]
  84. 84. 
    Badger S, Brønnum-Hansen C, Hartanto HB, Peraro T. Phys. Rev. Lett. 120:092001 2018.
     [Google Scholar]
  85. 85. 
    Abreu S et al. J. High Energy Phys. 1811:116 2018.
     [Google Scholar]
  86. 86. 
    Dunbar DC, Godwin JH, Perkins WB, Strong JM. Phys. Rev. D 101:016009 2020.
     [Google Scholar]
  87. 87. 
    Bern Z, Carrasco J, Johansson H. Phys. Rev. D 78:085011 2008.
     [Google Scholar]
  88. 88. 
    Bern Z, Carrasco JJM, Johansson H. Phys. Rev. Lett. 105:061602 2010.
     [Google Scholar]
  89. 89. 
    Bern Z et al. arXiv:1909.01358 [hep-th] 2019.
     [Google Scholar]
  90. 90. 
    Arkani-Hamed N et al. J. High Energy Phys. 1101:41 2011.
     [Google Scholar]
  91. 91. 
    Arkani-Hamed N et al. Grassmannian Geometry of Scattering AmplitudesCambridge, UK: Cambridge Univ. Press 2016.Planar loop integrand of super Yang–Mills from positive Grassmannian.
     [Google Scholar]
  92. 92. 
    Franco S, Galloni D, Penante B, Wen C. J. High Energy Phys. 1506:199 2015.
     [Google Scholar]
  93. 93. 
    Benincasa P, Gordo D. J. High Energy Phys. 1711:192 2017.
     [Google Scholar]
  94. 94. 
    Henn J, Mistlberger B, Smirnov VA, Wasser P. J. High Energy Phys. 2004:167 2020.
     [Google Scholar]
  95. 95. 
    Arkani-Hamed N, Bourjaily JL, Cachazo F, Trnka J. Phys. Rev. Lett. 113:261603 2014.
     [Google Scholar]
  96. 96. 
    Arkani-Hamed N, Trnka J. J. High Energy Phys. 1410:30 2014.Amplituhedron: dual geometric definition of planar loop integrands in super Yang–Mills.
     [Google Scholar]
  97. 97. 
    Goncharov AB, Spradlin M, Vergu C, Volovich A. Phys. Rev. Lett. 105:151605 2010.
     [Google Scholar]
  98. 98. 
    Jegerlehner F, Nyffeler A. Phys. Rep. 477:1 2009.
     [Google Scholar]
  99. 99. 
    Abreu S, Britto R, Duhr C, Gardi E. Phys. Rev. Lett. 119:051601 2017.
     [Google Scholar]
  100. 100. 
    Del Duca V, Duhr C, Smirnov VA. J. High Energy Phys. 1005:84 2010.
     [Google Scholar]
  101. 101. 
    Golden J et al. J. High Energy Phys. 1401:91 2014.
     [Google Scholar]
  102. 102. 
    Gehrmann T, Remiddi E. Nucl. Phys. B 580:485 2000.
     [Google Scholar]
  103. 103. 
    Henn JM. Phys. Rev. Lett. 110:251601 2013.Novel method for computing Feynman integrals.
     [Google Scholar]
  104. 104. 
    Duhr C. J. Phys. A Math. Theor. 44:15 2011.
     [Google Scholar]
  105. 105. 
    Lee RN. J. High Energy Phys. 1504:108 2015.
     [Google Scholar]
  106. 106. 
    Meyer C. J. High Energy Phys. 1704:6 2017.
     [Google Scholar]
  107. 107. 
    Prausa M. Comput. Phys. Commun. 219:361 2017.
     [Google Scholar]
  108. 108. 
    Gituliar O, Magerya V. Comput. Phys. Commun. 219:329 2017.
     [Google Scholar]
  109. 109. 
    Dlapa C, Henn J, Yan K. J. High Energy Phys. 2005:25 2020.
     [Google Scholar]
  110. 110. 
    Henn JM. J. Phys. A Math. Theor. 48:153001 2015.
     [Google Scholar]
  111. 111. 
    Duhr C. J. High Energy Phys. 1208:43 2012.
     [Google Scholar]
  112. 112. 
    Duhr C, Dulat F. J. High Energy Phys. 1908:135 2019.
     [Google Scholar]
  113. 113. 
    Caola F, Henn JM, Melnikov K, Smirnov VA. J. High Energy Phys. 1409:43 2014.
     [Google Scholar]
  114. 114. 
    Gehrmann T, von Manteuffel A, Tancredi L, Weihs E. J. High Energy Phys. 1406:32 2014.
     [Google Scholar]
  115. 115. 
    Gehrmann T et al. Phys. Rev. Lett. 113:212001 2014.
     [Google Scholar]
  116. 116. 
    Weinzierl S. Phys. Rev. D 84:074007 2011.
     [Google Scholar]
  117. 117. 
    Anastasiou C, Sterman G. J. High Energy Phys. 1907:56 2019.
     [Google Scholar]
  118. 118. 
    Hannesdottir H, Schwartz MD arXiv:1906.03271 [hep-th] 2019.
     [Google Scholar]
  119. 119. 
    Henn JM, Peraro T, Stahlhofen M, Wasser P. Phys. Rev. Lett. 122:201602 2019.
     [Google Scholar]
  120. 120. 
    von Manteuffel A, Panzer E, Schabinger RM. J. High Energy Phys. 1502:120 2015.
     [Google Scholar]
  121. 121. 
    Bourjaily JL et al. J. High Energy Phys. 1203:32 2012.
     [Google Scholar]
  122. 122. 
    Bourjaily JL, Trnka J. J. High Energy Phys. 1508:119 2015.
     [Google Scholar]
  123. 123. 
    Caron-Huot S, Henn JM. J. High Energy Phys. 1406:114 2014.
     [Google Scholar]
  124. 124. 
    Lipstein AE, Mason L. J. High Energy Phys. 1401:169 2014.
     [Google Scholar]
  125. 125. 
    Herrmann E, Parra-Martinez J. J. High Energy Phys. 2002:99 2020.
     [Google Scholar]
  126. 126. 
    Basham C, Brown LS, Ellis SD, Love ST. Phys. Rev. Lett. 41:1585 1978.
     [Google Scholar]
  127. 127. 
    Henn J, Sokatchev E, Yan K, Zhiboedov A. Phys. Rev. D 100:036010 2019.
     [Google Scholar]
  128. 128. 
    Hofman DM, Maldacena J. J. High Energy Phys. 0805:012 2008.Energy–energy correlation in super Yang–Mills.
     [Google Scholar]
  129. 129. 
    Kologlu M, Kravchuk P, Simmons-Duffin D, Zhiboedov A arXiv:1905.01311 [hep-th] 2019.
     [Google Scholar]
  130. 130. 
    Dixon LJ et al. Phys. Rev. Lett. 120:102001 2018.
     [Google Scholar]
  131. 131. 
    Luo MX, Shtabovenko V, Yang TZ, Zhu HX. J. High Energy Phys. 1906:37 2019.
     [Google Scholar]
  132. 132. 
    Korchemsky G. J. High Energy Phys. 2001:8 2020.
     [Google Scholar]
  133. 133. 
    Dixon LJ, Moult I, Zhu HX. Phys. Rev. D 100:014009 2019.
     [Google Scholar]
  134. 134. 
    Chen H et al. J. High Energy Phys. 2008:28 2020.
     [Google Scholar]
  135. 135. 
    Chen H, Moult I, Zhang X, Zhu HX. Phys. Rev. D 102:054012 2020.
     [Google Scholar]
  136. 136. 
    Chicherin D, Henn J, Sokatchev E, Yan K arXiv:2001.10806 [hep-th] 2020.
     [Google Scholar]
  137. 137. 
    Eden RJ, Landshoff PV, Olive DI, Polkinghorne JC The Analytic S-Matrix Cambridge, UK: Cambridge Univ. Press 1966.
     [Google Scholar]
  138. 138. 
    Bern Z, Dixon LJ, Dunbar DC, Kosower DA. Nucl. Phys. B 425:217 1994.
     [Google Scholar]
  139. 139. 
    Dixon LJ, Drummond JM, Henn JM. J. High Energy Phys. 1111:23 2011.
     [Google Scholar]
  140. 140. 
    Caron-Huot S, Dixon LJ, McLeod A, von Hippel M. Phys. Rev. Lett. 117:241601 2016.Steinmann relations applied to bootstrap.
     [Google Scholar]
  141. 141. 
    Caron-Huot S et al. J. High Energy Phys. 1908:16 2019.
     [Google Scholar]
  142. 142. 
    Basso B, Caron-Huot S, Sever A. J. High Energy Phys. 1501:27 2015.
     [Google Scholar]
  143. 143. 
    Drummond J, Foster J, Gurdogan O. Phys. Rev. Lett. 120:161601 2018.
     [Google Scholar]
  144. 144. 
    Dixon LJ et al. J. High Energy Phys. 1702:137 2017.
     [Google Scholar]
  145. 145. 
    Drummond J, Foster J, Gurdogan O, Papathanasiou G. J. High Energy Phys. 1903:87 2019.
     [Google Scholar]
  146. 146. 
    Li Y, Zhu HX. Phys. Rev. Lett. 118:022004 2017.
     [Google Scholar]
  147. 147. 
    Almelid O et al. J. High Energy Phys. 1709:73 2017.
     [Google Scholar]
  148. 148. 
    Drummond J et al. J. High Energy Phys. 1308:133 2013.
     [Google Scholar]
  149. 149. 
    Chicherin D, Henn J, Mitev V. J. High Energy Phys. 1805:164 2018.
     [Google Scholar]
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What Can We Learn About QCD and Collider Physics from N=4 Super Yang–Mills?
Annual Review of Nuclear and Particle Science 71, 87 (2021); https://doi.org/10.1146/annurev-nucl-102819-100428
/content/journals/10.1146/annurev-nucl-102819-100428
/content/journals/10.1146/annurev-nucl-102819-100428
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