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Notes on the scattering amplitude – Wilson loop duality. (English) Zbl 1298.81357
Summary: We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We extend the duality to amplitudes with arbitrary helicity states by introducing a suitable supersymmetric extension of the Wilson loop. We show that this object is determined by a host of recursion relations, which are valid at tree level and at loop level for a certain “loop integrand” defined within the Lagrangian insertion procedure. These recursion relations reproduce the BCFW ones obeyed by tree-level scattering amplitudes, as well as their extension to loop integrands which appeared recently in the literature, establishing the duality to all orders in perturbation theory. Finally, we propose that a certain set of finite correlation functions can be used to compute all first derivatives of the logarithm of MHV amplitudes.

81U20 \(S\)-matrix theory, etc. in quantum theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
81T18 Feynman diagrams
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[1] Minahan, JA; Zarembo, K., The Bethe-ansatz for \(N\) = 4 super Yang-Mills, JHEP, 03, 013, (2003)
[2] N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. (2007) P01021 [hep-th/0610251] [SPIRES].
[3] Maldacena, JM, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113, (1999)
[4] Green, MB; Schwarz, JH; Brink, L., \(N\) = 4 Yang-Mills and \(N\) = 8 supergravity as limits of string theories, Nucl. Phys., B 198, 474, (1982)
[5] Bern, Z.; Czakon, M.; Dixon, LJ; Kosower, DA; Smirnov, VA, The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory, Phys. Rev., D 75, 085010, (2007)
[6] Drummond, JM; Henn, J.; Smirnov, VA; Sokatchev, E., Magic identities for conformal four-point integrals, JHEP, 01, 064, (2007)
[7] Bern, Z.; Dixon, LJ; Smirnov, VA, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev., D 72, 085001, (2005)
[8] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., On planar gluon amplitudes/Wilson loops duality, Nucl. Phys., B 795, 52, (2008)
[9] Alday, LF; Maldacena, JM, Gluon scattering amplitudes at strong coupling, JHEP, 06, 064, (2007)
[10] Alday, LF; Maldacena, J., Comments on gluon scattering amplitudes via AdS/CFT, JHEP, 11, 068, (2007)
[11] Bartels, J.; Lipatov, LN; Sabio Vera, A., BFKL pomeron, reggeized gluons and Bern-Dixon-Smirnov amplitudes, Phys. Rev., D 80, 045002, (2009)
[12] Berkovits, N.; Maldacena, J., Fermionic T-duality, dual superconformal symmetry and the amplitude/Wilson loop connection, JHEP, 09, 062, (2008)
[13] Alday, LF; Roiban, R., Scatteringamplitudes, Wilson loops and the string/gauge theory correspondence, Phys. Rept., 468, 153, (2008)
[14] Korchemsky, GP; Drummond, JM; Sokatchev, E., Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys., B 795, 385, (2008)
[15] Brandhuber, A.; Heslop, P.; Travaglini, G., MHV amplitudes in \(N\) = 4 super Yang-Mills and Wilson loops, Nucl. Phys., B 794, 231, (2008)
[16] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude, Phys. Lett., B 662, 456, (2008)
[17] Bern, Z.; etal., The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang-Mills theory, Phys. Rev., D 78, 045007, (2008)
[18] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys., B 815, 142, (2009)
[19] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., Dual superconformal symmetry of scattering amplitudes in \(N\) = 4 super-Yang-Mills theory, Nucl. Phys., B 828, 317, (2010)
[20] Brandhuber, A.; Heslop, P.; Travaglini, G., A note on dual superconformal symmetry of the \(N\) = 4 super Yang-Mills S-matrix, Phys. Rev., D 78, 125005, (2008)
[21] A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [SPIRES].
[22] Mason, LJ; Skinner, D., Dual superconformal invariance, momentum twistors and Grassmannians, JHEP, 11, 045, (2009)
[23] Arkani-Hamed, N.; Cachazo, F.; Cheung, C., The Grassmannian origin of dual superconformal invariance, JHEP, 03, 036, (2010)
[24] Drummond, JM; Henn, JM; Plefka, J., Yangian symmetry of scattering amplitudes in \(N\) = 4 super Yang-Mills theory, JHEP, 05, 046, (2009)
[25] Korchemsky, GP; Sokatchev, E., Symmetries and analytic properties of scattering amplitudes in \(N\) = 4 SYM theory, Nucl. Phys., B 832, 1, (2010)
[26] Alday, LF; Henn, JM; Plefka, J.; Schuster, T., Scattering into the fifth dimension of \(N\) = 4 super Yang-Mills, JHEP, 01, 077, (2010)
[27] Mason, LJ; Skinner, D., The complete planar \(S\)-matrix of \(N\) = 4 SYM as a Wilson loop in twistor space, JHEP, 12, 018, (2010)
[28] Mason, L.; Skinner, D., Amplitudes at weak coupling as polytopes in ads_{5}, J. Phys., A 44, 135401, (2011)
[29] B. Eden, G.P. Korchemsky and E. Sokatchev, More on the duality correlators/amplitudes, arXiv:1009.2488 [SPIRES].
[30] B. Eden, G.P. Korchemsky and E. Sokatchev, From correlation functions to scattering amplitudes, arXiv:1007.3246 [SPIRES].
[31] Arkani-Hamed, N.; Bourjaily, JL; Cachazo, F.; Caron-Huot, S.; Trnka, J., The all-loop integrand for scattering amplitudes in planar \(N\) = 4 SYM, JHEP, 01, 041, (2011)
[32] Caron-Huot, S., Loops and trees, JHEP, 05, 080, (2011)
[33] Nair, VP, A current algebra for some gauge theory amplitudes, Phys. Lett., B 214, 215, (1988)
[34] Bullimore, M.; Mason, LJ; Skinner, D., MHV diagrams in momentum twistor space, JHEP, 12, 032, (2010)
[35] Chalmers, G.; Siegel, W., The self-dual sector of QCD amplitudes, Phys. Rev., D 54, 7628, (1996)
[36] Elvang, H.; Freedman, DZ; Kiermaier, M., Dual conformal symmetry of 1-loop NMHV amplitudes in N = 4 SYM theory, JHEP, 03, 075, (2010)
[37] N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local integrals for planar scattering amplitudes, arXiv:1012.6032 [SPIRES].
[38] A. Hodges, The box integrals in momentum-twistor geometry, arXiv:1004.3323 [SPIRES].
[39] Mason, L.; Skinner, D., Amplitudes at weak coupling as polytopes in AdS_{5}, J. Phys., A 44, 135401, (2011)
[40] Drummond, JM; Henn, JM, Simple loop integrals and amplitudes in \(N\) = 4 SYM, JHEP, 05, 105, (2011)
[41] L.F. Alday, Some analytic results for two-loop scattering amplitudes, arXiv:1009.1110 [SPIRES].
[42] Korchemsky, GP; Sokatchev, E., Superconformal invariants for scattering amplitudes in \(N\) = 4 SYM theory, Nucl. Phys., B 839, 377, (2010)
[43] Drummond, JM; Ferro, L., The yangian origin of the Grassmannian integral, JHEP, 12, 010, (2010)
[44] L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, arXiv:1007.3243 [SPIRES].
[45] Britto, R.; Cachazo, F.; Feng, B., New recursion relations for tree amplitudes of gluons, Nucl. Phys., B 715, 499, (2005)
[46] Britto, R.; Cachazo, F.; Feng, B.; Witten, E., Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett., 94, 181602, (2005)
[47] Drummond, JM; Henn, JM, All tree-level amplitudes in \(N\) = 4 SYM, JHEP, 04, 018, (2009)
[48] Intriligator, KA, Bonus symmetries of N = 4 super-Yang-Mills correlation functions via AdS duality, Nucl. Phys., B 551, 575, (1999)
[49] Eden, B.; Petkou, AC; Schubert, C.; Sokatchev, E., Partial non-renormalisation of the stress-tensor four-point function in \(N\) = 4 SYM and AdS/CFT, Nucl. Phys., B 607, 191, (2001)
[50] Eden, B.; Schubert, C.; Sokatchev, E., Three-loop four-point correlator in \(N\) = 4 SYM, Phys. Lett., B 482, 309, (2000)
[51] Petkou, A.; Skenderis, K., A non-renormalization theorem for conformal anomalies, Nucl. Phys., B 561, 100, (1999)
[52] Howe, PS; Schubert, C.; Sokatchev, E.; West, PC, Explicit construction of nilpotent covariants in \(N\) = 4 SYM, Nucl. Phys., B 571, 71, (2000)
[53] Weinberg, S., Six-dimensional methods for four-dimensional conformal field theories, Phys. Rev. D, 82, 045031, (2010)
[54] Goncharov, AB; Spradlin, M.; Vergu, C.; Volovich, A., Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett., 105, 151605, (2010)
[55] Henn, JM; Naculich, SG; Schnitzer, HJ; Spradlin, M., More loops and legs in Higgs-regulated \(N\) = 4 SYM amplitudes, JHEP, 08, 002, (2010)
[56] Bern, Z.; Rozowsky, JS; Yan, B., Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills, Phys. Lett., B 401, 273, (1997)
[57] A.V. Belitsky, G.P. Korchemsky and E. Sokatchev, Are scattering amplitudes dual to super Wilson loops?, arXiv:1103.3008 [SPIRES].
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