Higher loop mixed correlators in \( \mathcal{N} = 4\) SYM. (English) Zbl 1342.81538
Summary: We compute analytically the two-loop contribution to the correlation function of the Lagrangian with a four-sided light-like (or null) Wilson loop in \(N = 4\) super Yang-Mills. As a non-trivial test of our result, we reproduce the three-loop value of the cusp anomalous dimension upon integration over the insertion point of the Lagrangian. The method we used involved calculating a dual scattering amplitude. Moreover, we give a simple representation of the loop integrand of the latter in twistor variables.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
Keywords:
duality in gauge field theories; scattering amplitudes; Wilson, ’t Hooft and Polyakov loopsReferences:
| [1] | 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] [INSPIRE]. |
| [2] | L. Alday, E. Buchbinder and A. Tseytlin, Correlation function of null polygonal Wilson loops with local operators, JHEP09 (2011) 034 [arXiv:1107.5702] [INSPIRE]. · Zbl 1301.81095 · doi:10.1007/JHEP09(2011)034 |
| [3] | O.T. Engelund and R. Roiban, On correlation functions of Wilson loops, local and non-local operators, JHEP05 (2012) 158 [arXiv:1110.0758] [INSPIRE]. · Zbl 1348.81317 · doi:10.1007/JHEP05(2012)158 |
| [4] | I. Korchemskaya and G. Korchemsky, On lightlike Wilson loops, Phys. Lett.B 287 (1992) 169 [INSPIRE]. |
| [5] | J. Drummond, J. Henn, G. 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]. · Zbl 1203.81175 · doi:10.1016/j.nuclphysb.2009.10.013 |
| [6] | L.F. Alday, P. Heslop and J. Sikorowski, Perturbative correlation functions of null Wilson loops and local operators, arXiv:1207.4316 [INSPIRE]. · Zbl 1342.81250 |
| [7] | L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, JHEP09 (2011) 123 [arXiv:1007.3243] [INSPIRE]. · Zbl 1301.81096 · doi:10.1007/JHEP09(2011)123 |
| [8] | B. Eden, G.P. Korchemsky and E. Sokatchev, From correlation functions to scattering amplitudes, JHEP12 (2011) 002 [arXiv:1007.3246] [INSPIRE]. · Zbl 1306.81096 · doi:10.1007/JHEP12(2011)002 |
| [9] | L.F. Alday, J.M. Henn, J. Plefka and T. Schuster, Scattering into the fifth dimension of \(\mathcal{N} =4\) super Yang-Mills, JHEP01(2010)077[arXiv:0908.0684][INSPIRE]. · Zbl 1269.81079 · doi:10.1007/JHEP01(2010)077 |
| [10] | J.M. Henn, S. Moch and S.G. Naculich, Form factors and scattering amplitudes in \(\mathcal{N} = 4\) SYM in dimensional and massive regularizations, JHEP12 (2011) 024 [arXiv:1109.5057] [INSPIRE]. · Zbl 1306.81111 · doi:10.1007/JHEP12(2011)024 |
| [11] | J.M. Drummond and J.M. Henn, Simple loop integrals and amplitudes in \(\mathcal{N} = 4\) SYM, JHEP05 (2011) 105 [arXiv:1008.2965] [INSPIRE]. · Zbl 1296.81058 · doi:10.1007/JHEP05(2011)105 |
| [12] | L.J. Dixon, J.M. Drummond and J.M. Henn, Analytic result for the two-loop six-point NMHV amplitude in \(\mathcal{N} = 4\) super Yang-Mills theory, JHEP01 (2012) 024 [arXiv:1111.1704] [INSPIRE]. · Zbl 1306.81093 · doi:10.1007/JHEP01(2012)024 |
| [13] | A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [INSPIRE]. · Zbl 1342.81291 |
| [14] | L. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and grassmannians, JHEP11 (2009) 045 [arXiv:0909.0250] [INSPIRE]. · doi:10.1088/1126-6708/2009/11/045 |
| [15] | N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The all-loop integrand for scattering amplitudes in planar \(\mathcal{N} = 4\) SYM, JHEP01 (2011) 041 [arXiv:1008.2958] [INSPIRE]. · Zbl 1214.81141 · doi:10.1007/JHEP01(2011)041 |
| [16] | N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local integrals for planar scattering amplitudes, JHEP06 (2012) 125 [arXiv:1012.6032] [INSPIRE]. · Zbl 1397.81428 · doi:10.1007/JHEP06(2012)125 |
| [17] | J.M. Drummond, J.M. Henn and J. Trnka, New differential equations for on-shell loop integrals, JHEP04 (2011) 083 [arXiv:1010.3679] [INSPIRE]. · Zbl 1250.81064 · doi:10.1007/JHEP04(2011)083 |
| [18] | L.F. Alday, Some analytic results for two-loop scattering amplitudes, JHEP07 (2011) 080 [arXiv:1009.1110] [INSPIRE]. · Zbl 1298.81355 · doi:10.1007/JHEP07(2011)080 |
| [19] | B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in \(\mathcal{N} = 4\) SYM, Nucl. Phys.B 862 (2012) 450 [arXiv:1201.5329] [INSPIRE]. · Zbl 1246.81363 · doi:10.1016/j.nuclphysb.2012.04.013 |
| [20] | J.L. Bourjaily, A. DiRe, A. Shaikh, M. Spradlin and A. Volovich, The soft-collinear bootstrap:\( \mathcal{N} = 4\) Yang-Mills amplitudes at six and seven loops, JHEP03 (2012) 032 [arXiv:1112.6432] [INSPIRE]. · Zbl 1309.81145 · doi:10.1007/JHEP03(2012)032 |
| [21] | J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, Higgs-regularized three-loop four-gluon amplitude in \(\mathcal{N} = 4\) SYM: exponentiation and Regge limits, JHEP 04 (2010) 038 [arXiv:1001.1358] [INSPIRE]. · Zbl 1272.81117 · doi:10.1007/JHEP04(2010)038 |
| [22] | T. Gehrmann and E. Remiddi, Using differential equations to compute two loop box integrals, Nucl. Phys. Proc. Suppl.89 (2000) 251 [hep-ph/0005232] [INSPIRE]. · Zbl 1071.81089 · doi:10.1016/S0920-5632(00)00851-3 |
| [23] | S. Caron-Huot and K.J. Larsen, Uniqueness of two-loop master contours, JHEP10 (2012) 026 [arXiv:1205.0801] [INSPIRE]. · doi:10.1007/JHEP10(2012)026 |
| [24] | S. Gubser, I. Klebanov and A.M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys.B 636 (2002) 99 [hep-th/0204051] [INSPIRE]. · Zbl 0996.81076 · doi:10.1016/S0550-3213(02)00373-5 |
| [25] | S. Frolov and A.A. Tseytlin, Semiclassical quantization of rotating superstring in AdS5× S5, JHEP06 (2002) 007 [hep-th/0204226] [INSPIRE]. · doi:10.1088/1126-6708/2002/06/007 |
| [26] | T. Adamo, Correlation functions, null polygonal Wilson loops and local operators, JHEP12 (2011)006 [arXiv:1110.3925] [INSPIRE]. · Zbl 1306.81067 · doi:10.1007/JHEP12(2011)006 |
| [27] | V.A. Smirnov, Feynman integral calculus, Springer, Berlin Germay (2006). · Zbl 1111.81003 |
| [28] | E. Remiddi and J. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys.A 15 (2000) 725 [hep-ph/9905237] [INSPIRE]. · Zbl 0951.33003 |
| [29] | D. Maître, HPL, a Mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun.174 (2006) 222 [hep-ph/0507152] [INSPIRE]. · Zbl 1196.68330 · doi:10.1016/j.cpc.2005.10.008 |
| [30] | J. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys.A 14 (1999)2037 [hep-ph/9806280] [INSPIRE]. · Zbl 0939.65032 |
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