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Loop lessons from Wilson loops in \(\mathcal{N} = 4\) supersymmetric Yang-Mills theory. (English) Zbl 1294.81082
Summary: \(\mathcal{N} = 4\) supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple one-and two-parametric integrals over a single propagator in configuration space. We observe that the two-loop Wilson-loop “hard-diagram” corresponds to a four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of the configuration-space propagator and loop Feynman diagrams, we derive Feynman parameterizations of complicated planar and non-planar Feynman diagrams which simplify their evaluation. For illustration, we compute numerically a four-loop hexagon scalar Feynman diagram.
81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T18 Feynman diagrams
81U05 \(2\)-body potential quantum scattering theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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[1] Maldacena, JM, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113, (1999)
[2] Minahan, JA; Zarembo, K., The Bethe-ansatz for N =4 super Yang-Mills, JHEP, 03, 013, (2003)
[3] Beisert, N.; Frolov, S.; Staudacher, M.; Tseytlin, AA, Precision spectroscopy of AdS/CFT, JHEP, 10, 037, (2003)
[4] Beisert, N.; Staudacher, M., Long-range PSU(2, 2-4) Bethe ansaetze for gauge theory and strings, Nucl. Phys., B 727, 1, (2005)
[5] Anastasiou, C.; Bern, Z.; Dixon, LJ; Kosower, DA, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett., 91, 251602, (2003)
[6] 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)
[7] Cachazo, F.; Spradlin, M.; Volovich, A., Iterative structure within the five-particle two-loop amplitude, Phys. Rev., D 74, 045020, (2006)
[8] Bern, Z.; Czakon, M.; Kosower, DA; Roiban, R.; Smirnov, VA, Two-loop iteration of five-point \( \mathcal{N} = 4 \) super-Yang-Mills amplitudes, Phys. Rev. Lett., 97, 181601, (2006)
[9] Bern, Z.; etal., The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang-Mills theory, Phys. Rev., D 78, 045007, (2008)
[10] Alday, LF; Maldacena, JM, Gluon scattering amplitudes at strong coupling, JHEP, 06, 064, (2007)
[11] Korchemsky, GP; Drummond, JM; Sokatchev, E., Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B, 795, 385, (2008)
[12] Brandhuber, A.; Heslop, P.; Travaglini, G., MHV amplitudes in \( \mathcal{N} = 4 \) super Yang-Mills and Wilson loops, Nucl. Phys., B 794, 231, (2008)
[13] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys., B 815, 142, (2009)
[14] Brandhuber, A.; etal., A surprise in the amplitude/Wilson loop duality, JHEP, 07, 080, (2010)
[15] Duca, V.; Duhr, C.; Smirnov, VA, An analytic result for the two-loop hexagon Wilson loop in \( \mathcal{N} = 4 \) SYM, JHEP, 03, 099, (2010)
[16] Duca, V.; Duhr, C.; Smirnov, VA, The two-loop hexagon Wilson loop in \( \mathcal{N} = 4 \) SYM, JHEP, 05, 084, (2010)
[17] Anastasiou, C.; etal., Two-loop polygon Wilson loops in \( \mathcal{N} = 4 \) SYM, JHEP, 05, 115, (2009)
[18] Green, MB; Schwarz, JH; Brink, L., \( \mathcal{N} = 4 \) Yang-Mills and \( \mathcal{N} = 8 \) supergravity as limits of string theories, Nucl. Phys., B 198, 474, (1982)
[19] Bern, Z.; Rozowsky, JS; Yan, B., Two-loop four-gluon amplitudes in \( \mathcal{N} = 4 \) super-Yang-Mills, Phys. Lett., B 401, 273, (1997)
[20] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys., B 826, 337, (2010)
[21] Duca, V.; Duhr, C.; Smirnov, VA, A two-loop octagon Wilson loop in \( \mathcal{N} = 4 \) SYM, JHEP, 09, 015, (2010)
[22] Gorsky, A.; Zhiboedov, A., One-loop derivation of the Wilson polygon — MHV amplitude duality, J. Phys., A 42, 355214, (2009)
[23] Gorsky, A.; Zhiboedov, A., Aspects of the \( \mathcal{N} = 4 \) SYM amplitude — Wilson polygon duality, Nucl. Phys., B 835, 343, (2010)
[24] Tausk, JB, Non-planar massless two-loop Feynman diagrams with four on-shell legs, Phys. Lett., B 469, 225, (1999)
[25] Kramer, G.; Lampe, B., Integrals for two loop calculations in massless QCD, J. Math. Phys., 28, 945, (1987)
[26] Boos, EE; Davydychev, AI, A method of the evaluation of the vertex type Feynman integrals, Moscow Univ. Phys. Bull., 42, 6, (1987)
[27] Davydychev, AI, Recursive algorithm of evaluating vertex type Feynman integrals, J. Phys., A 25, 5587, (1992)
[28] Anastasiou, C.; Glover, EWN; Oleari, C., Scalar one-loop integrals using the negative-dimension approach, Nucl. Phys., B 572, 307, (2000)
[29] Anastasiou, C.; Glover, EWN; Oleari, C., Application of the negative-dimension approach to massless scalar box integrals, Nucl. Phys., B 565, 445, (2000)
[30] Binoth, T.; Heinrich, G., An automatized algorithm to compute infrared divergent multi-loop integrals, Nucl. Phys., B 585, 741, (2000)
[31] C. Anastasiou, F. Herzog and A. Lazopoulos, On the factorization of overlapping singularities at NNLO, arXiv:1011.4867 [SPIRES].
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