×

zbMATH — the first resource for mathematics

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.
MSC:
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
PDF BibTeX Cite
Full Text: DOI arXiv
References:
[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].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.