References
Published online by Cambridge University Press: 05 January 2015
HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
Information
- Type
- Chapter
- Information
- Scattering Amplitudes in Gauge Theory and Gravity , pp. 299 - 318Publisher: Cambridge University PressPrint publication year: 2015
- Creative Commons
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC 4.0 https://creativecommons.org/cclicenses/
References
Mangano, M. L. and Parke, S. J., “Multiparton amplitudes in gauge theories,” Phys. Rept. 200, 301 (1991) [hep-th/0509223].CrossRefGoogle Scholar
Srednicki, M., Quantum Field Theory, Cambridge, UK: Cambridge University Press (2007).CrossRefGoogle Scholar
Dixon, L. J., “Calculating scattering amplitudes efficiently,” In Boulder 1995, QCD and beyond, 539–582 [hep-ph/9601359].Google Scholar
Dixon, L. J., “Scattering amplitudes: the most perfect microscopic structures in the universe,” J. Phys. A 44, 454001 (2011) [arXiv:1105.0771 [hep-th]].Google Scholar
Parke, S. J. and Taylor, T. R., “An amplitude for n gluon scattering,” Phys. Rev. Lett. 56, 2459 (1986).CrossRefGoogle ScholarPubMed
Kampf, K., Novotny, J., and Trnka, J., “Tree-level amplitudes in the nonlinear sigma model,” JHEP 1305, 032 (2013) [arXiv:1304.3048 [hep-th]].Google Scholar
Kleiss, R. and Kuijf, H., “Multi-gluon cross-sections and five jet production at hadron colliders,” Nucl. Phys. B 312, 616 (1989).10.1016/0550-3213(89)90574-9CrossRefGoogle Scholar
Del Duca, V., Dixon, L. J., and Maltoni, F., “New color decompositions for gauge amplitudes at tree and loop level,” Nucl. Phys. B 571, 51 (2000) [hep-ph/9910563].CrossRefGoogle Scholar
Bern, Z., Carrasco, J. J. M., and Johansson, H., “New relations for gauge-theory amplitudes,” Phys. Rev. D 78, 085011 (2008) [arXiv:0805.3993 [hep-ph]].10.1103/PhysRevD.78.085011CrossRefGoogle Scholar
Berger, C. F., Del Duca, V., and Dixon, L. J., “Recursive construction of Higgs-plus-multiparton loop amplitudes: The last of the phi-nite loop amplitudes,” Phys. Rev. D 74, 094021 (2006) [Erratum-ibid. D 76, 099901 (2007)] [hep-ph/0608180]Google ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Dixon, L. J., “A brief introduction to modern amplitude methods,” [arXiv:1310.5353 [hep-ph]].Google Scholar
Berends, F. A. and Giele, W. T., “Recursive calculations for processes with n gluons,” Nucl. Phys. B 306, 759 (1988).Google ScholarGoogle Scholar
Britto, R., Cachazo, F., and Feng, B., “New recursion relations for tree amplitudes of gluons,” Nucl. Phys. B 715, 499 (2005) [hep-th/0412308].CrossRefGoogle Scholar
Britto, R., Cachazo, F., Feng, B., and Witten, E., “Direct proof of tree-level recursion relation in Yang–Mills theory,” Phys. Rev. Lett. 94, 181602 (2005) [hep-th/0501052].10.1103/PhysRevLett.94.181602CrossRefGoogle ScholarPubMed
Cachazo, F., Svrcek, P., and Witten, E., “MHV vertices and tree amplitudes in gauge theory,” JHEP 0409, 006 (2004) [hep-th/0403047].Google Scholar
Feng, B., Wang, J., Wang, Y., and Zhang, Z., “BCFW recursion relation with nonzero boundary contribution,” JHEP 1001, 019 (2010) [arXiv:0911.0301 [hep-th]].Google Scholar
Conde, E. and Rajabi, S., “The twelve-graviton next-to-MHV amplitude from Risager’s construction,” JHEP 1209, 120 (2012) [arXiv:1205.3500 [hep-th]].Google Scholar
Arkani-Hamed, N. and Kaplan, J., “On tree amplitudes in gauge theory and gravity,” JHEP 0804, 076 (2008) [arXiv:0801.2385 [hep-th]].Google Scholar
Cheung, C., “On-shell recursion relations for generic theories,” JHEP 1003, 098 (2010) [arXiv:0808.0504 [hep-th]].Google Scholar
Benincasa, P., Boucher-Veronneau, C., and Cachazo, F., “Taming tree amplitudes in general relativity,” JHEP 0711, 057 (2007) [hep-th/0702032 [HEP-TH]].Google Scholar
Kawai, H., Lewellen, D. C., and Tye, S. H. H., “A relation between tree amplitudes of closed and open strings,” Nucl. Phys. B 269, 1 (1986).CrossRefGoogle Scholar
Sannan, S., “Gravity as the limit of the type II superstring theory,” Phys. Rev. D 34, 1749 (1986).CrossRefGoogle Scholar
Arkani-Hamed, N., Cachazo, F., Cheung, C., and Kaplan, J., “A duality for the S matrix,” JHEP 1003, 020 (2010) [arXiv:0907.5418 [hep-th]].Google Scholar
Hodges, A., “Eliminating spurious poles from gauge-theoretic amplitudes,” JHEP 1305, 135 (2013) [arXiv:0905.1473 [hep-th]].Google Scholar
Spradlin, M., Volovich, A., and Wen, C., “Three applications of a bonus relation for gravity amplitudes,” Phys. Lett. B 674, 69 (2009) [arXiv:0812.4767 [hep-th]].10.1016/j.physletb.2009.02.059CrossRefGoogle Scholar
Cohen, T., Elvang, H., and Kiermaier, M., “On-shell constructibility of tree amplitudes in general field theories,” JHEP 1104, 053 (2011) [arXiv:1010.0257 [hep-th]].Google Scholar
Elvang, H., Freedman, D. Z., and Kiermaier, M., “Recursion relations, generating functions, and unitarity sums in N = 4 SYM theory,” JHEP 0904, 009 (2009) [arXiv:0808.1720 [hep-th]].Google Scholar
Risager, K., “A direct proof of the CSW rules,” JHEP 0512, 003 (2005) [hep-th/ 0508206].Google Scholar
Elvang, H., Freedman, D. Z., and Kiermaier, M., “Proof of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory,” JHEP 0906, 068 (2009) [arXiv:0811.3624 [hep-th]].Google Scholar
Dixon, L. J., Glover, E. W. N., and Khoze, V. V., “MHV rules for Higgs plus multi-gluon amplitudes,” JHEP 0412, 015 (2004) [hep-th/0411092].Google Scholar
Badger, S. D., Glover, E. W. N., and Khoze, V. V., “MHV rules for Higgs plus multiparton amplitudes,” JHEP 0503, 023 (2005) [hep-th/0412275].Google Scholar
Brandhuber, A., Spence, B., and Travaglini, G., “Tree-level formalism,” J. Phys. A 44, 454002 (2011) [arXiv:1103.3477 [hep-th]].CrossRefGoogle Scholar
Gorsky, A. and Rosly, A., “From Yang–Mills Lagrangian to MHV diagrams,” JHEP 0601, 101 (2006) [hep-th/0510111]Google ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Boels, R., Mason, L. J., and Skinner, D., “From twistor actions to MHV diagrams,” Phys. Lett. B 648, 90 (2007) [hep-th/0702035].CrossRefGoogle Scholar
Bjerrum-Bohr, N. E. J., Dunbar, D. C., Ita, H., Perkins, W. B., and Risager, K., “MHV-vertices for gravity amplitudes,” JHEP 0601, 009 (2006) [hep-th/0509016].Google Scholar
Bianchi, M., Elvang, H., and Freedman, D. Z., “Generating tree amplitudes in N = 4 SYM and N = 8 SG,” JHEP 0809, 063 (2008) [arXiv:0805.0757 [hep-th]].Google Scholar
Wess, J. and Bagger, J., Supersymmetry and Supergravity, Princeton, USA: University Press (1992).Google Scholar
Grisaru, M. T. and Pendleton, H. N., “Some properties of scattering amplitudes in supersymmetric theories,” Nucl. Phys. B 124, 81 (1977)10.1016/0550-3213(77)90277-2Google ScholarGoogle Scholar
Freedman, D. Z. and Van Proeyen, A., Supergravity, Cambridge, UK: Cambridge University Press (2012).10.1017/CBO9781139026833CrossRefGoogle Scholar
Brink, L., Schwarz, J. H., and Scherk, J., “Supersymmetric Yang–Mills theories,” Nucl. Phys. B 121, 77 (1977).10.1016/0550-3213(77)90328-5CrossRefGoogle Scholar
Ferber, A., “Supertwistors and conformal supersymmetry,” Nucl. Phys. B 132, 55 (1978).CrossRefGoogle Scholar
Elvang, H., Freedman, D. Z., and Kiermaier, M., “Solution to the Ward identities for superamplitudes,” JHEP 1010, 103 (2010) [arXiv:0911.3169 [hep-th]].Google Scholar
Elvang, H., Freedman, D. Z., and Kiermaier, M., “SUSY Ward identities, superamplitudes, and counterterms,” J. Phys. A 44, 454009 (2011) [arXiv:1012.3401 [hep-th]].10.1088/1751-8113/44/45/454009CrossRefGoogle Scholar
Kiermaier, M. and Naculich, S. G., “A super MHV vertex expansion for N = 4 SYM theory,” JHEP 0905, 072 (2009) [arXiv:0903.0377 [hep-th]].Google Scholar
Arkani-Hamed, N., “What is the simplest QFT?,” talk given at the Paris Workshop Wonders of Gauge Theory and Supergravity, 24 June 2008.Google Scholar
Brandhuber, A., Heslop, P., and Travaglini, G., “A note on dual superconformal symmetry of the N = 4 super Yang–Mills S-matrix,” Phys. Rev. D 78, 125005 (2008) [arXiv:0807.4097 [hep-th]].CrossRefGoogle Scholar
Arkani-Hamed, N., Cachazo, F., and Kaplan, J., “What is the simplest quantum field theory?,” JHEP 1009, 016 (2010) [arXiv:0808.1446 [hep-th]].Google Scholar
Bern, Z., Carrasco, J. J. M., Ita, H., Johansson, H., and Roiban, R., “On the structure of supersymmetric sums in multi-loop unitarity cuts,” Phys. Rev. D 80, 065029 (2009) [arXiv:0903.5348 [hep-th]].10.1103/PhysRevD.80.065029CrossRefGoogle Scholar
Drummond, J. M. and Henn, J. M., “All tree-level amplitudes in N = 4 SYM,” JHEP 0904, 018 (2009) [arXiv:0808.2475 [hep-th]].CrossRefGoogle Scholar
Drummond, J. M., Henn, J., Korchemsky, G. P., and Sokatchev, E., “Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang–Mills theory,” Nucl. Phys. B 828, 317 (2010) [arXiv:0807.1095 [hep-th]].CrossRefGoogle Scholar
Drummond, J. M., Spradlin, M., Volovich, A., and Wen, C., “Tree-level amplitudes in N = 8 supergravity,” Phys. Rev. D 79, 105018 (2009) [arXiv:0901.2363 [hep-th]].CrossRefGoogle Scholar
Drummond, J. M., “Hidden simplicity of gauge theory amplitudes,” Class. Quant. Grav. 27, 214001 (2010) [arXiv:1010.2418 [hep-th]].10.1088/0264-9381/27/21/214001CrossRefGoogle Scholar
Penrose, R., “Twistor algebra,” J. Math. Phys. 8, 345 (1967).10.1063/1.1705200CrossRefGoogle Scholar
Witten, E., “Perturbative gauge theory as a string theory in twistor space,” Commun. Math. Phys. 252, 189 (2004) [hep-th/0312171].CrossRefGoogle Scholar
Dirac, P. A. M., “Wave equations in conformal space,” Annals Math. 37, 429 (1936).CrossRefGoogle Scholar
Siegel, W., “Embedding versus 6D twistors,” [arXiv:1204.5679 [hep-th]].Google Scholar
Siegel, W., “Fields,” [hep-th/9912205].Google Scholar
Drummond, J. M., Henn, J., Smirnov, V. A., and Sokatchev, E., “Magic identities for conformal four-point integrals,” JHEP 0701, 064 (2007) [hep-th/0607160].Google Scholar
Drummond, J. M., Henn, J. M., and Plefka, J., “Yangian symmetry of scattering amplitudes in N = 4 super Yang–Mills theory,” JHEP 0905, 046 (2009) [arXiv:0902.2987 [hep-th]].Google Scholar
Mason, L. J. and Skinner, D., “Dual superconformal invariance, momentum twistors and grassmannians,” JHEP 0911, 045 (2009) [arXiv:0909.0250 [hep-th]].Google ScholarGoogle ScholarGoogle Scholar
Roiban, R., “Review of AdS/CFT integrability, Chapter V.1: Scattering amplitudes –a brief introduction,” Lett. Math. Phys. 99, 455 (2012) [arXiv:1012.4001 [hep-th]].CrossRefGoogle Scholar
Magnea, Lorenzo, Lecture notes on Perturbative QCD at the National School of Theoretical Physics of the University of Parma (2008). http://personalpages.to.infn.it/∼magnea/QCD.pdfGoogle Scholar
Bork, L. V., Kazakov, D. I., Vartanov, G. S., and Zhiboedov, A. V., “Construction of infrared finite observables in N = 4 super Yang–Mills theory,” Phys. Rev. D 81, 105028 (2010) [arXiv:0911.1617 [hep-th]].10.1103/PhysRevD.81.105028CrossRefGoogle Scholar
Bern, Z., Chalmers, G., Dixon, L. J., and Kosower, D. A., “One loop N gluon amplitudes with maximal helicity violation via collinear limits,” Phys. Rev. Lett. 72, 2134 (1994) [hep-ph/9312333].CrossRefGoogle ScholarPubMed
Mahlon, G., “Multi-gluon helicity amplitudes involving a quark loop,” Phys. Rev. D 49, 4438 (1994) [hep-ph/9312276].Google ScholarPubMed
Bern, Z., Dixon, L. J., and Kosower, D. A., “Dimensionally regulated pentagon integrals,” Nucl. Phys. B 412, 751 (1994) [hep-ph/9306240].10.1016/0550-3213(94)90398-0CrossRefGoogle Scholar
Bern, Z., Dixon, L. J., Dunbar, D. C., and Kosower, D. A., “One loop n point gauge theory amplitudes, unitarity and collinear limits,” Nucl. Phys. B 425, 217 (1994) [hep-ph/9403226]Google ScholarGoogle Scholar
Carrasco, J. J. M. and Johansson, H., “Generic multiloop methods and application to N = 4 super-Yang–Mills,” J. Phys. A 44, 454004 (2011) [arXiv:1103.3298 [hep-th]].10.1088/1751-8113/44/45/454004CrossRefGoogle Scholar
Bern, Z. and Y.-t. Huang, “Basics of generalized unitarity,” J. Phys. A 44, 454003 (2011) [arXiv:1103.1869 [hep-th]].10.1088/1751-8113/44/45/454003CrossRefGoogle Scholar
Ita, H., “Susy theories and QCD: Numerical approaches,” J. Phys. A 44, 454005 (2011) [arXiv:1109.6527 [hep-th]].10.1088/1751-8113/44/45/454005CrossRefGoogle Scholar
Britto, R., “Loop amplitudes in gauge theories: Modern analytic approaches,” J. Phys. A 44, 454006 (2011) [arXiv:1012.4493 [hep-th]].10.1088/1751-8113/44/45/454006CrossRefGoogle Scholar
van Neerven, W. L. and Vermaseren, J. A. M., “Large loop integrals,” Phys. Lett. B 137, 241 (1984).CrossRefGoogle Scholar
Bern, Z., Dixon, L. J., and Kosower, D. A., “Dimensionally regulated one loop integrals,” Phys. Lett. B 302, 299 (1993) [Erratum-ibid. B 318, 649 (1993)] [hep-ph/9212308].CrossRefGoogle Scholar
Bern, Z., Dixon, L. J., and Kosower, D. A., “Dimensionally regulated pentagon integrals,” Nucl. Phys. B 412, 751 (1994) [hep-ph/9306240].10.1016/0550-3213(94)90398-0CrossRefGoogle Scholar
Brown, L. M. and Feynman, R. P., “Radiative corrections to Compton scattering,” Phys. Rev. 85, 231 (1952)10.1103/PhysRev.85.231Google ScholarGoogle Scholar
Passarino, G. and Veltman, M. J. G., “One loop corrections for e+ e− annihilation into mu+ mu− in the Weinberg model,” Nucl. Phys. B 160, 151 (1979).10.1016/0550-3213(79)90234-7CrossRefGoogle Scholar
Ellis, R. K., Kunszt, Z., Melnikov, K., and Zanderighi, G., “One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts,” Phys. Rept. 518, 141 (2012) [arXiv:1105.4319 [hep-ph]].CrossRefGoogle Scholar
Johansson, H., Kosower, D. A., and Larsen, K. J., “An overview of maximal unitarity at two loops,” PoS LL 2012, 066 (2012) [arXiv:1212.2132 [hep-th]].Google Scholar
Anastasiou, C., Britto, R., Feng, B., Kunszt, Z., and Mastrolia, P., “D-dimensional unitarity cut method,” Phys. Lett. B 645, 213 (2007) [hep-ph/0609191]Google ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Bern, Z. and Morgan, A. G., “Massive loop amplitudes from unitarity,” Nucl. Phys. B 467, 479 (1996) [hep-ph/9511336]10.1016/0550-3213(96)00078-8Google ScholarGoogle Scholar
Badger, S. D., “Direct extraction of one loop rational terms,” JHEP 0901, 049 (2009) [0806.4600 [hep-ph]].Google Scholar
Green, M. B., Schwarz, J. H., and Brink, L., “N = 4 Yang–Mills and N = 8 supergravity as limits of string theories,” Nucl. Phys. B 198, 474 (1982).10.1016/0550-3213(82)90336-4CrossRefGoogle Scholar
Bern, Z., Bjerrum-Bohr, N. E. J., and Dunbar, D. C., “Inherited twistor-space structure of gravity loop amplitudes,” JHEP 0505, 056 (2005) [hep-th/0501137]Google ScholarGoogle ScholarGoogle Scholar
Bern, Z., Carrasco, J. J., Forde, D., Ita, H., and Johansson, H., “Unexpected cancellations in gravity theories,” Phys. Rev. D 77, 025010 (2008) [arXiv:0707.1035 [hep-th]].CrossRefGoogle Scholar
Lal, S. and Raju, S., “The next-to-simplest quantum field theories,” Phys. Rev. D 81, 105002 (2010) [arXiv:0910.0930 [hep-th]].10.1103/PhysRevD.81.105002CrossRefGoogle Scholar
Dunbar, D. C., Ettle, J. H., and Perkins, W. B., “Perturbative expansion of N <8 supergravity,” Phys. Rev. D 83, 065015 (2011) [arXiv:1011.5378 [hep-th]].10.1103/PhysRevD.83.065015CrossRefGoogle Scholar
Elvang, H., Y.-t. Huang, and Peng, C., “On-shell superamplitudes in N <4 SYM,” JHEP 1109, 031 (2011) [arXiv:1102.4843 [hep-th]].Google Scholar
Huang, Y.-t., McGady, D. A., and Peng, C., “One-loop renormalization and the S-matrix,” [arXiv:1205.5606 [hep-th]].Google Scholar
Marcus, N., “Composite anomalies in supergravity,” Phys. Lett. B 157, 383 (1985).10.1016/0370-2693(85)90385-5CrossRefGoogle Scholar
di Vecchia, P., Ferrara, S., and Girardello, L., “Anomalies of hidden local chiral symmetries in sigma models and extended supergravities,” Phys. Lett. B 151, 199 (1985).10.1016/0370-2693(85)90834-2CrossRefGoogle Scholar
Drummond, J. M., Henn, J., Korchemsky, G. P., and Sokatchev, E., “Generalized unitarity for N = 4 super-amplitudes,” Nucl. Phys. B 869, 452 (2013) [arXiv:0808.0491 [hep-th]].10.1016/j.nuclphysb.2012.12.009CrossRefGoogle Scholar
Brandhuber, A., Heslop, P., and Travaglini, G., “One-loop amplitudes in N = 4 super Yang–Mills and anomalous dual conformal symmetry,” JHEP 0908, 095 (2009) [arXiv:0905.4377 [hep-th]].Google Scholar
Elvang, H., Freedman, D. Z., and Kiermaier, M., “Dual conformal symmetry of 1-loop NMHV amplitudes in N = 4 SYM theory,” JHEP 1003, 075 (2010) [arXiv:0905.4379 [hep-th]].Google Scholar
Korchemsky, G. P. and Sokatchev, E., “Symmetries and analytic properties of scattering amplitudes in N = 4 SYM theory,” Nucl. Phys. B 832, 1 (2010) [arXiv:0906.1737 [hep-th]].10.1016/j.nuclphysb.2010.01.022CrossRefGoogle Scholar
Gluza, J., Kajda, K., and Kosower, D. A., “Towards a basis for planar two-loop integrals,” Phys. Rev. D 83, 045012 (2011) [arXiv:1009.0472 [hep-th]].10.1103/PhysRevD.83.045012CrossRefGoogle Scholar
Kosower, D. A. and Larsen, K. J., “Maximal unitarity at two loops,” Phys. Rev. D 85, 045017 (2012) [arXiv:1108.1180 [hep-th]]10.1103/PhysRevD.85.045017Google ScholarGoogle Scholar
Badger, S., Frellesvig, H., and Zhang, Y., “Hepta-cuts of two-loop scattering amplitudes,” JHEP 1204, 055 (2012) [arXiv:1202.2019 [hep-ph]].Google Scholar
Zhang, Y., “Integrand-level reduction of loop amplitudes by computational algebraic geometry methods,” JHEP 1209, 042 (2012) [arXiv:1205.5707 [hep-ph]].Google Scholar
Sgaard, M., “Global residues and two-loop hepta-cuts,” JHEP 1309, 116 (2013) [arXiv:1306.1496 [hep-th]].Google Scholar
Smirnov, A. V. and Petukhov, A. V., “The number of master integrals is finite,” Lett. Math. Phys. 97, 37 (2011) [arXiv:1004.4199 [hep-th]].10.1007/s11005-010-0450-0CrossRefGoogle Scholar
Anastasiou, C., Bern, Z., Dixon, L. J., and Kosower, D. A., “Planar amplitudes in maximally supersymmetric Yang–Mills theory,” Phys. Rev. Lett. 91, 251602 (2003) [hep-th/0309040].10.1103/PhysRevLett.91.251602CrossRefGoogle ScholarPubMed
Bern, Z., Dixon, L. J., and Smirnov, V. A., “Iteration of planar amplitudes in maximally supersymmetric Yang–Mills theory at three loops and beyond,” Phys. Rev. D 72, 085001 (2005) [hep-th/0505205].10.1103/PhysRevD.72.085001CrossRefGoogle Scholar
Bern, Z., Rozowsky, J. S., and Yan, B., “Two loop four gluon amplitudes in N = 4 superYang–Mills,” Phys. Lett. B 401, 273 (1997) [hep-ph/9702424].Google Scholar
Bern, Z., Czakon, M., Kosower, D. A., Roiban, R., and Smirnov, V. A., “Two-loop iteration of five-point N = 4 super-Yang–Mills amplitudes,” Phys. Rev. Lett. 97, 181601 (2006) [hep-th/0604074].10.1103/PhysRevLett.97.181601CrossRefGoogle ScholarPubMed
Cachazo, F., Spradlin, M., and Volovich, A., “Iterative structure within the five-particle two-loop amplitude,” Phys. Rev. D 74, 045020 (2006) [hep-th/0602228].10.1103/PhysRevD.74.045020CrossRefGoogle Scholar
Alday, L. F. and Maldacena, J., “Comments on gluon scattering amplitudes via AdS/CFT,” JHEP 0711, 068 (2007) [arXiv:0710.1060 [hep-th]].Google Scholar
Alday, L. F. and Maldacena, J. M., “Gluon scattering amplitudes at strong coupling,” JHEP 0706, 064 (2007) [arXiv:0705.0303 [hep-th]].Google Scholar
Bern, Z., Dixon, L. J., Kosower, D. A., et al., “The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang–Mills theory,” Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465 [hep-th]].10.1103/PhysRevD.78.045007CrossRefGoogle Scholar
Cachazo, F., Spradlin, M., and Volovich, A., “Leading singularities of the two-loop six-particle MHV amplitude,” Phys. Rev. D 78, 105022 (2008) [arXiv:0805.4832 [hep-th]].10.1103/PhysRevD.78.105022CrossRefGoogle Scholar
Del Duca, V., Duhr, C., and Smirnov, V. A., “An analytic result for the two-loop hexagon Wilson loop in N = 4 SYM,” JHEP 1003, 099 (2010) [arXiv:0911.5332 [hep-ph]].Google Scholar
Del Duca, V., Duhr, C., and Smirnov, V. A., “The two-loop hexagon Wilson loop in N = 4 SYM,” JHEP 1005, 084 (2010) [arXiv:1003.1702 [hep-th]].Google Scholar
Goncharov, A. B., Spradlin, M., Vergu, C., and Volovich, A., “Classical polylogarithms for amplitudes and Wilson loops,” Phys. Rev. Lett. 105, 151605 (2010) [arXiv:1006.5703 [hep-th]].10.1103/PhysRevLett.105.151605CrossRefGoogle ScholarPubMed
Nigel Glover, E. W. and Williams, C., “One-loop gluonic amplitudes from single unitarity cuts,” JHEP 0812, 067 (2008) [0810.2964 [hep-th]]Google ScholarGoogle ScholarGoogle Scholar
Arkani-Hamed, N., Bourjaily, J. L., Cachazo, F., Caron-Huot, S., and Trnka, J., “The all-loop integrand for scattering amplitudes in planar N = 4 SYM,” JHEP 1101, 041 (2011) [arXiv:1008.2958 [hep-th]].Google Scholar
Boels, R. H., “On BCFW shifts of integrands and integrals,” JHEP 1011, 113 (2010) [arXiv:1008.3101 [hep-th]].Google Scholar
Bern, Z., Carrasco, J. J. M., Johansson, H., and Kosower, D. A., “Maximally supersymmetric planar Yang–Mills amplitudes at five loops,” Phys. Rev.D 76, 125020 (2007) [0705.1864 [hep-th]].CrossRefGoogle Scholar
Britto, R., Cachazo, F., and Feng, B., “Generalized unitarity and one-loop amplitudes in N = 4 super-Yang–Mills,” Nucl. Phys. B 725, 275 (2005) [hep-th/0412103]10.1016/j.nuclphysb.2005.07.014Google ScholarGoogle Scholar
Arkani-Hamed, N., Bourjaily, J. L., Cachazo, F., and Trnka, J., “Local integrals for planar scattering amplitudes,” JHEP 1206, 125 (2012) [arXiv:1012.6032 [hep-th]].Google ScholarGoogle Scholar
Arkani-Hamed, N., Bourjaily, J. L., Cachazo, F., et al., “Scattering amplitudes and the positive Grassmannian,” [arXiv:1212.5605 [hep-th]].Google Scholar
Cachazo, F., “Sharpening the leading singularity,” [arXiv:0803.1988 [hep-th]].Google Scholar
Drummond, J. M. and Ferro, L., “Yangians, Grassmannians and T-duality,” JHEP 1007, 027 (2010) [arXiv:1001.3348 [hep-th]].Google Scholar
Drummond, J. M. and Ferro, L., “The Yangian origin of the Grassmannian integral,” JHEP 1012, 010 (2010) [arXiv:1002.4622 [hep-th]]Google ScholarGoogle Scholar
Roiban, R., Spradlin, M., and Volovich, A., “On the tree level S matrix of Yang–Mills theory,” Phys. Rev. D 70, 026009 (2004) [hep-th/0403190].10.1103/PhysRevD.70.026009CrossRefGoogle Scholar
Spradlin, M. and Volovich, A., “From twistor string theory to recursion relations,” Phys. Rev. D 80, 085022 (2009) [arXiv:0909.0229 [hep-th]].10.1103/PhysRevD.80.085022CrossRefGoogle Scholar
Arkani-Hamed, N., Bourjaily, J., Cachazo, F., and Trnka, J., “Unification of residues and Grassmannian dualities,” JHEP 1101, 049 (2011) [arXiv:0912.4912 [hep-th]].Google Scholar
Bourjaily, J. L., Trnka, J., Volovich, A., and Wen, C., “The Grassmannian and the twistor string: Connecting all trees in N = 4 SYM,” JHEP 1101, 038 (2011) [arXiv:1006.1899 [hep-th]].Google Scholar
Bullimore, M., Mason, L. J., and Skinner, D., “Twistor-strings, Grassmannians and leading singularities,” JHEP 1003, 070 (2010) [arXiv:0912.0539 [hep-th]].Google Scholar
Dolan, L. and Goddard, P., “Complete equivalence between gluon tree amplitudes in twistor string theory and in gauge theory,” JHEP 1206, 030 (2012) [arXiv:1111.0950 [hep-th]].Google Scholar
Arkani-Hamed, N., Bourjaily, J. L., Cachazo, F., Hodges, A., and Trnka, J., “A note on polytopes for scattering amplitudes,” JHEP 1204, 081 (2012) [arXiv:1012.6030 [hep-th]].Google Scholar
Bullimore, M., Mason, L. J., and Skinner, D., “MHV diagrams in momentum twistor space,” JHEP 1012, 032 (2010) [arXiv:1009.1854 [hep-th]].Google Scholar
Arkani-Hamed, N. and Trnka, J., “The amplituhedron,” [arXiv:1312.2007 [hep-th]]Google ScholarGoogle Scholar
Mason, L. and Skinner, D., “Amplitudes at weak coupling as polytopes in AdS5,” J. Phys. A 44, 135401 (2011) [arXiv:1004.3498 [hep-th]].10.1088/1751-8113/44/13/135401CrossRefGoogle Scholar
Nastase, H. and Schnitzer, H. J., “Twistor and polytope interpretations for subleading color one-loop amplitudes,” Nucl. Phys. B 855, 901 (2012) [arXiv:1104.2752 [hep-th]].10.1016/j.nuclphysb.2011.10.029CrossRefGoogle Scholar
Boels, R., “Covariant representation theory of the Poincare´ algebra and some of its extensions,” JHEP 1001, 010 (2010) [arXiv:0908.0738 [hep-th]].Google Scholar
Caron-Huot, S. and O’Connell, D., “Spinor helicity and dual conformal symmetry in ten dimensions,” JHEP 1108, 014 (2011) [arXiv:1010.5487 [hep-th]].Google Scholar
Boels, R. H. and O’Connell, D., “Simple superamplitudes in higher dimensions,” JHEP 1206, 163 (2012) [arXiv:1201.2653 [hep-th]].Google Scholar
Davies, S., “One-loop QCD and Higgs to partons processes using six-dimensional helicity and generalized unitarity,” Phys. Rev. D 84, 094016 (2011) [arXiv:1108.0398 [hep-ph]].10.1103/PhysRevD.84.094016CrossRefGoogle Scholar
Bern, Z., Carrasco, J. J., Dennen, T., Y.-t. Huang, and Ita, H., “Generalized unitarity and six-dimensional helicity,” Phys. Rev. D 83, 085022 (2011) [arXiv:1010.0494 [hep-th]].10.1103/PhysRevD.83.085022CrossRefGoogle Scholar
Craig, N., Elvang, H., Kiermaier, M., and Slatyer, T., “Massive amplitudes on the Coulomb branch of N = 4 SYM,” JHEP 1112, 097 (2011) [arXiv:1104.2050 [hep-th]].Google Scholar
Cheung, C. and O’Connell, D., “Amplitudes and spinor-helicity in six dimensions,” JHEP 0907, 075 (2009) [arXiv:0902.0981 [hep-th]].Google Scholar
Dennen, T., Y.-t. Huang, and Siegel, W., “Supertwistor space for 6D maximal super Yang–Mills,” JHEP 1004, 127 (2010) [arXiv:0910.2688 [hep-th]].Google Scholar
Brandhuber, A., Korres, D., Koschade, D., and Travaglini, G., “One-loop amplitudes in six-dimensional (1,1) theories from generalised unitarity,” JHEP 1102, 077 (2011) [arXiv:1010.1515 [hep-th]]Google ScholarGoogle Scholar
Dennen, T. and Y.-t. Huang, “Dual conformal properties of six-dimensional maximal super Yang–Mills amplitudes,” JHEP 1101, 140 (2011) [arXiv:1010.5874 [hep-th]].Google Scholar
Chern, T., “Superconformal field theory in six dimensions and supertwistor,” [arXiv:0906.0657 [hep-th]]Google ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Czech, B., Y.-t. Huang, and Rozali, M., “Amplitudes for multiple M5 branes,” JHEP 1210, 143 (2012) [arXiv:1110.2791 [hep-th]].Google Scholar
Saemann, C. and Wolf, M., “Non-Abelian tensor multiplet equations from twistor space,” [arXiv:1205.3108 [hep-th]].Google Scholar
Huang, Y.-t. and Lipstein, A. E., “Amplitudes of 3D and 6D maximal superconformal theories in supertwistor space,” JHEP 1010, 007 (2010) [arXiv:1004.4735 [hep-th]].Google Scholar
Alday, L. F., Henn, J. M., Plefka, J., and Schuster, T., “Scattering into the fifth dimension of N = 4 super Yang–Mills,” JHEP 1001, 077 (2010) [arXiv:0908.0684 [hep-th]].Google Scholar
Agarwal, A., Beisert, N., and McLoughlin, T., “Scattering in mass-deformed N ≥ 4 Chern–Simons models,” JHEP 0906, 045 (2009) [arXiv:0812.3367 [hep-th]].Google Scholar
Gustavsson, A., “Algebraic structures on parallel M2-branes,” Nucl. Phys. B 811, 66 (2009) [arXiv:0709.1260 [hep-th]].10.1016/j.nuclphysb.2008.11.014CrossRefGoogle Scholar
Bagger, J. and Lambert, N., “Gauge symmetry and supersymmetry of multiple M2-branes,” Phys. Rev. D 77, 065008 (2008) [arXiv:0711.0955 [hep-th]].10.1103/PhysRevD.77.065008CrossRefGoogle Scholar
Bandres, M. A., Lipstein, A. E., and Schwarz, J. H., “N = 8 superconformal Chern–Simons theories,” JHEP 0805, 025 (2008) [arXiv:0803.3242 [hep-th]].Google Scholar
Gomis, J., Milanesi, G., and Russo, J. G., “Bagger-Lambert theory for general Lie algebras,” JHEP 0806, 075 (2008) [arXiv:0805.1012 [hep-th]].Google Scholar
Benvenuti, S., Rodriguez-Gomez, D., Tonni, E., and Verlinde, H., “N = 8 supercon-formal gauge theories and M2 branes,” JHEP 0901, 078 (2009) [arXiv:0805.1087 [hep-th]].Google Scholar
Ho, P. -M., Imamura, Y., and Matsuo, Y., “M2 to D2 revisited,” JHEP 0807, 003 (2008) [arXiv:0805.1202 [hep-th]].Google Scholar
Bargheer, T., Loebbert, F., and Meneghelli, C., “Symmetries of tree-level scattering amplitudes in N = 6 superconformal Chern–Simons theory,” Phys. Rev. D 82, 045016 (2010) [arXiv:1003.6120 [hep-th]].10.1103/PhysRevD.82.045016CrossRefGoogle Scholar
Aharony, O., Bergman, O., Jafferis, D. L., and Maldacena, J., “N = 6 superconformal Chern–Simons-matter theories, M2-branes and their gravity duals,” JHEP 0810, 091 (2008) [arXiv:0806.1218 [hep-th]].Google Scholar
Benna, M., Klebanov, I., Klose, T., and Smedback, M., “Superconformal Chern– Simons theories and AdS(4)/CFT(3) correspondence,” JHEP 0809, 072 (2008) [arXiv:0806.1519 [hep-th]].Google Scholar
Bandres, M. A., Lipstein, A. E., and Schwarz, J. H., “Studies of the ABJM theory in a formulation with manifest SU(4) R-symmetry,” JHEP 0809, 027 (2008) [arXiv:0807.0880 [hep-th]].Google Scholar
Gustavsson, A., “Selfdual strings and loop space Nahm equations,” JHEP 0804, 083 (2008) [arXiv:0802.3456 [hep-th]]Google ScholarGoogle Scholar
Gang, D., Y.-t. Huang, Koh, E., Lee, S., and A. E. Lipstein, “Tree-level recursion relation and dual superconformal symmetry of the ABJM theory,” JHEP 1103, 116 (2011) [arXiv:1012.5032 [hep-th]].Google Scholar
Huang, Y.-t. and Lipstein, A. E., “Dual superconformal symmetry of N = 6 Chern– Simons theory,” JHEP 1011, 076 (2010) [arXiv:1008.0041 [hep-th]].Google Scholar
Bargheer, T., Beisert, N., Loebbert, F., and McLoughlin, T., “Conformal anomaly for amplitudes in N = 6 superconformal Chern–Simons theory,” J. Phys. A 45, 475402 (2012) [arXiv:1204.4406 [hep-th]].10.1088/1751-8113/45/47/475402CrossRefGoogle Scholar
Bianchi, M. S., Leoni, M., Mauri, A., Penati, S., and Santambrogio, A., “One loop amplitudes In ABJM,” JHEP 1207, 029 (2012) [arXiv:1204.4407 [hep-th]].Google Scholar
Brandhuber, A., Travaglini, G., and Wen, C., “All one-loop amplitudes in N = 6 superconformal Chern–Simons theory,” JHEP 1210, 145 (2012) [arXiv:1207.6908 [hep-th]].Google Scholar
Chen, W. -M. and Huang, Y.-t., “Dualities for loop amplitudes of N = 6 Chern–Simons matter theory,” JHEP 1111, 057 (2011) [arXiv:1107.2710 [hep-th]];Google Scholar
Brandhuber, A., Travaglini, G., and Wen, C., “A note on amplitudes in N = 6 supercon-formal Chern–Simons theory,” JHEP 1207, 160 (2012) [arXiv:1205.6705 [hep-th]].Google Scholar
Bianchi, M. S., Leoni, M., Mauri, A., Penati, S., and Santambrogio, A., “Scattering amplitudes/Wilson loop duality in ABJM theory,” JHEP 1201, 056 (2012) [arXiv:1107.3139 [hep-th]].Google Scholar
Caron-Huot, S. and Y.-t. Huang, “The two-loop six-point amplitude in ABJM theory,” JHEP 1303, 075 (2013) [arXiv:1210.4226 [hep-th]].Google Scholar
Lee, S., “Yangian invariant scattering amplitudes in supersymmetric Chern–Simons theory,” Phys. Rev. Lett. 105, 151603 (2010) [arXiv:1007.4772 [hep-th]].10.1103/PhysRevLett.105.151603CrossRefGoogle ScholarPubMed
Huang, Y. -t., Wen, C., and Xie, D., “The positive orthogonal Grassmannian and loop amplitudes of ABJM,” [arXiv:1402.1479 [hep-th]].Google Scholar
Huang, Y.-t. and Lee, S., “A new integral formula for supersymmetric scattering amplitudes in three dimensions,” Phys. Rev. Lett. 109, 191601 (2012) [arXiv:1207.4851 [hep-th]].CrossRefGoogle ScholarPubMed
Engelund, O. T. and Roiban, R., “A twistor string for the ABJ(M) theory,” [arXiv:1401.6242 [hep-th]].Google Scholar
Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, USA: John Wiley & Sons (1972).Google Scholar
Wald, R. M., General Relativity, Chicago, USA: University Press (1984).10.7208/chicago/9780226870373.001.0001CrossRefGoogle Scholar
Carroll, S. M., Spacetime and Geometry: An Introduction to General Relativity, San Francisco, USA: Addison-Wesley (2004).Google Scholar
DeWitt, B. S., “Quantum theory of gravity. 2. The manifestly covariant theory,” Phys. Rev. 162, 1195 (1967)Google ScholarGoogle ScholarGoogle Scholar
Berends, F. A., Giele, W. T., and Kuijf, H., “On relations between multi-gluon and multigraviton scattering,” Phys. Lett. B 211, 91 (1988).10.1016/0370-2693(88)90813-1CrossRefGoogle Scholar
Bedford, J., Brandhuber, A., Spence, B. J., and Travaglini, G., “A recursion relation for gravity amplitudes,” Nucl. Phys. B 721, 98 (2005) [hep-th/0502146].10.1016/j.nuclphysb.2005.05.016CrossRefGoogle Scholar
Elvang, H. and Freedman, D. Z., “Note on graviton MHV amplitudes,” JHEP 0805, 096 (2008) [arXiv:0710.1270 [hep-th]].Google Scholar
Nguyen, D., Spradlin, M., Volovich, A., and Wen, C., “The tree formula for MHV graviton amplitudes,” JHEP 1007, 045 (2010) [arXiv:0907.2276 [hep-th]].Google Scholar
Bern, Z., Dixon, L. J., Perelstein, M., and Rozowsky, J. S., “Multileg one loop gravity amplitudes from gauge theory,” Nucl. Phys. B 546, 423 (1999) [hep-th/9811140].10.1016/S0550-3213(99)00029-2CrossRefGoogle Scholar
Bern, Z. and Grant, A. K., “Perturbative gravity from QCD amplitudes,” Phys. Lett. B 457, 23 (1999) [hep-th/9904026].10.1016/S0370-2693(99)00524-9CrossRefGoogle Scholar
Bern, Z., Dixon, L. J., Dunbar, D. C., et al., “On perturbative gravity and gauge theory,” Nucl. Phys. Proc. Suppl. 88, 194 (2000) [hep-th/0002078].Google Scholar
Siegel, W., “Two vierbein formalism for string inspired axionic gravity,” Phys. Rev. D 47, 5453 (1993) [hep-th/9302036].CrossRefGoogle ScholarPubMed
Bern, Z., “Perturbative quantum gravity and its relation to gauge theory,” Living Rev. Rel. 5, 5 (2002) [gr-qc/0206071].10.12942/lrr-2002-5CrossRefGoogle ScholarPubMed
Freedman, D. Z., “Some beautiful equations of mathematical physics,” In ICTP (ed.): The Dirac Medals of the ICTP 1993 25–53, and CERN Geneva – TH.-7367 (94/07,rec.Sep.) [hep-th/9408175].Google Scholar
Gates, S. J., Grisaru, M. T., Rocek, M., and Siegel, W., “Superspace or one thousand and one lessons in supersymmetry,” Front. Phys. 58, 1 (1983) [hep-th/0108200].Google Scholar
de Wit, B. and Freedman, D. Z., “On SO(8) extended supergravity,” Nucl. Phys. B 130, 105 (1977).10.1016/0550-3213(77)90395-9CrossRefGoogle Scholar
Cremmer, E. and Julia, B., “The N = 8 supergravity theory. 1. The Lagrangian,” Phys. Lett. B 80, 48 (1978)10.1016/0370-2693(78)90303-9Google ScholarGoogle Scholar
de Wit, B. and Nicolai, H., “N = 8 supergravity,” Nucl. Phys. B 208, 323 (1982).10.1016/0550-3213(82)90120-1CrossRefGoogle Scholar
Hodges, A., “A simple formula for gravitational MHV amplitudes,” [arXiv:1204.1930 [hep-th]].Google Scholar
Cachazo, F., Mason, L., and Skinner, D., “Gravity in twistor space and its Grassmannian formulation,” [arXiv:1207.4712 [hep-th]].Google Scholar
He, S., “A link representation for gravity amplitudes,” [arXiv:1207.4064 [hep-th]].Google Scholar
Cachazo, F. and Geyer, Y., “A ‘twistor string’ inspired formula for tree-level scattering amplitudes in N = 8 RA,” [arXiv:1206.6511 [hep-th]].Google Scholar
Skinner, D., “Twistor strings for N = 8 supergravity,” [arXiv:1301.0868 [hep-th]].Google Scholar
Cachazo, F., He, S., and Yuan, E. Y., “Scattering equations and KLT orthogonality,” [arXiv:1306.6575 [hep-th]].Google Scholar
Cachazo, F., He, S., and Yuan, E. Y., “Scattering of massless particles in arbitrary dimension,” [arXiv:1307.2199 [hep-th]].Google Scholar
Adler, S. L., “Consistency conditions on the strong interactions implied by a partially conserved axial vector current,” Phys. Rev. 137, B1022 (1965).10.1103/PhysRev.137.B1022CrossRefGoogle Scholar
Coleman, S. R., “Secret symmetry: An introduction to spontaneous symmetry break-down and gauge fields,” Subnucl. Ser. 11, 139 (1975).Google Scholar
Kiermaier, M., “The Coulomb-branch S-matrix from massless amplitudes,” [arXiv:1105.5385 [hep-th]].Google Scholar
Hooft, G. ’t and Veltman, M. J. G., “One loop divergencies in the theory of gravitation,” Annales Poincare´ Phys. Theor. A 20, 69 (1974).Google Scholar
Goroff, M. H. and Sagnotti, A., “Quantum gravity at two loops,” Phys. Lett. B 160, 81 (1985).10.1016/0370-2693(85)91470-4CrossRefGoogle Scholar
van de Ven, A. E. M., “Two loop quantum gravity,” Nucl. Phys. B 378, 309 (1992).10.1016/0550-3213(92)90011-YCrossRefGoogle Scholar
Deser, S. and van Nieuwenhuizen, P., “One loop divergences of quantized Einstein–Maxwell fields,” Phys. Rev. D 10, 401 (1974).Google Scholar
Grisaru, M. T., van Nieuwenhuizen, P., and Vermaseren, J. A. M., “One loop renormalizability of pure supergravity and of Maxwell–Einstein theory in extended supergravity,” Phys. Rev. Lett. 37, 1662 (1976).10.1103/PhysRevLett.37.1662CrossRefGoogle Scholar
Grisaru, M. T., “Two loop renormalizability of supergravity,” Phys. Lett. B 66, 75 (1977).10.1016/0370-2693(77)90617-7CrossRefGoogle Scholar
Tomboulis, E., “On the two loop divergences of supersymmetric gravitation,” Phys. Lett. B 67, 417 (1977).10.1016/0370-2693(77)90434-8CrossRefGoogle Scholar
Deser, S., Kay, J. H., and Stelle, K. S., “Renormalizability properties of supergravity,” Phys. Rev. Lett. 38, 527 (1977).10.1103/PhysRevLett.38.527CrossRefGoogle Scholar
Bern, Z., Dixon, L. J., and Roiban, R., “Is N = 8 supergravity ultraviolet finite?,” Phys. Lett. B 644, 265 (2007) [hep-th/0611086].10.1016/j.physletb.2006.11.030CrossRefGoogle Scholar
Bern, Z., Carrasco, J. J., Dixon, L. J., et al., “Three-loop superfiniteness of N = 8 supergravity,” Phys. Rev. Lett. 98, 161303 (2007) [hep-th/0702112].10.1103/PhysRevLett.98.161303CrossRefGoogle ScholarPubMed
Bern, Z., Carrasco, J. J. M., Dixon, L. J., Johansson, H., and Roiban, R., “Manifest ultraviolet behavior for the three-loop four-point amplitude of N = 8 supergravity,” Phys. Rev. D 78, 105019 (2008) [arXiv:0808.4112 [hep-th]].10.1103/PhysRevD.78.105019CrossRefGoogle Scholar
Howe, P. S. and Stelle, K. S., “Supersymmetry counterterms revisited,” Phys. Lett. B 554, 190 (2003) [hep-th/0211279].10.1016/S0370-2693(02)03271-9CrossRefGoogle Scholar
Bern, Z., Carrasco, J. J., Dixon, L. J., Johansson, H., and Roiban, R., “The ultraviolet behavior of N = 8 supergravity at four loops,” Phys. Rev. Lett. 103, 081301 (2009) [arXiv:0905.2326 [hep-th]].10.1103/PhysRevLett.103.081301CrossRefGoogle Scholar
Bern, Z., Carrasco, J. J. M., Dixon, L. J., Johansson, H., and Roiban, R., “The complete four-loop four-point amplitude in N = 4 super-Yang–Mills theory,” Phys. Rev. D 82, 125040 (2010) [arXiv:1008.3327 [hep-th]].10.1103/PhysRevD.82.125040CrossRefGoogle Scholar
Bjornsson, J. and Green, M. B., “5 loops in 24/5 dimensions,” JHEP 1008, 132 (2010) [arXiv:1004.2692 [hep-th]].Google Scholar
Elvang, H., Freedman, D. Z., and Kiermaier, M., “A simple approach to counterterms in N = 8 supergravity,” JHEP 1011, 016 (2010) [arXiv:1003.5018 [hep-th]].Google Scholar
Elvang, H. and Kiermaier, M., “Stringy KLT relations, global symmetries, and E7(7) violation,” JHEP 1010, 108 (2010) [arXiv:1007.4813 [hep-th]].Google Scholar
Beisert, N., Elvang, H., Freedman, D. Z., et al., “E7(7) constraints on counterterms in N = 8 supergravity,” Phys. Lett. B 694, 265 (2010) [arXiv:1009.1643 [hep-th]].10.1016/j.physletb.2010.09.069CrossRefGoogle Scholar
van Nieuwenhuizen, P. and Wu, C. C., “On integral relations for invariants constructed from three riemann tensors and their applications in quantum gravity,” J. Math. Phys. 18, 182 (1977).10.1063/1.523128CrossRefGoogle Scholar
Bossard, G., Hillmann, C., and Nicolai, H., “E7(7) symmetry in perturbatively quantised N = 8 supergravity,” JHEP 1012, 052 (2010) [arXiv:1007.5472 [hep-th]].Google Scholar
Freedman, D. Z. and Tonni, E., “The D2k R4 invariants of N = 8 supergravity,” JHEP 1104, 006 (2011) [arXiv:1101.1672 [hep-th]].Google Scholar
Deser, S. and Kay, J. H., “Three loop counterterms for extended supergravity,” Phys. Lett. B 76, 400 (1978).10.1016/0370-2693(78)90892-4CrossRefGoogle Scholar
Drummond, J. M., Heslop, P. J., and Howe, P. S., “A note on N = 8 counterterms,” [arXiv:1008.4939 [hep-th]].Google Scholar
Bossard, G. and Nicolai, H., “Counterterms vs. dualities,” JHEP 1108, 074 (2011) [arXiv:1105.1273 [hep-th]].Google Scholar
Kallosh, R. and Kugo, T., “The footprint of E(7(7)) amplitudes of N = 8 supergravity,” JHEP 0901, 072 (2009) [arXiv:0811.3414 [hep-th]]Google ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Stieberger, S. and Taylor, T. R., “Complete six-gluon disk amplitude in superstring theory,” Nucl. Phys. B 801, 128 (2008) [arXiv:0711.4354 [hep-th]].10.1016/j.nuclphysb.2008.04.026CrossRefGoogle Scholar
Broedel, J. and Dixon, L. J., “R∗∗4 counterterm and E(7)(7) symmetry in maximal supergravity,” JHEP 1005, 003 (2010) [arXiv:0911.5704 [hep-th]].Google Scholar
Berkovits, N., “New higher-derivative R∗∗4 theorems,” Phys. Rev. Lett. 98, 211601 (2007) [arXiv:hep-th/0609006]10.1103/PhysRevLett.98.211601Google ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Bern, Z., Carrasco, J. J. M., Dixon, L. J., Johansson, H., and Roiban, R., “Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes,” Phys. Rev. D 85, 105014 (2012) [arXiv:1201.5366 [hep-th]].10.1103/PhysRevD.85.105014CrossRefGoogle Scholar
Howe, P. S. and Lindstrom, U., “Higher order invariants in extended supergravity,” Nucl. Phys. B 181, 487 (1981).10.1016/0550-3213(81)90537-XCrossRefGoogle Scholar
Kallosh, R. E., “Counterterms in extended supergravities,” Phys. Lett. B 99, 122 (1981).10.1016/0370-2693(81)90964-3CrossRefGoogle Scholar
Bossard, G., Howe, P. S., Stelle, K. S., and Vanhove, P., “The vanishing volume of D = 4 superspace,” Class. Quant. Grav. 28, 215005 (2011) [arXiv:1105.6087 [hep-th]].10.1088/0264-9381/28/21/215005CrossRefGoogle Scholar
Berkovits, N., “Super Poincare´ covariant quantization of the superstring,” JHEP 0004, 018 (2000) [hep-th/0001035].Google Scholar
Green, M. B., Ooguri, H., and Schwarz, J. H., “Nondecoupling of maximal supergravity from the superstring,” Phys. Rev. Lett. 99, 041601 (2007) [arXiv:0704.0777 [hep-th]].10.1103/PhysRevLett.99.041601CrossRefGoogle ScholarPubMed
Banks, T., “Arguments against a finite N = 8 supergravity,” [arXiv:1205.5768 [hep-th]].Google Scholar
Bianchi, M., Ferrara, S., and Kallosh, R., “Perturbative and non-perturbative N = 8 supergravity,” Phys. Lett. B 690, 328 (2010) [arXiv:0910.3674 [hep-th]].10.1016/j.physletb.2010.05.049CrossRefGoogle Scholar
Bern, Z., Davies, S., Dennen, T., Y.-t. Huang, and Nohle, J., “Color-kinematics duality for pure Yang–Mills and gravity at one and two loops,” [arXiv:1303.6605 [hep-th]].Google Scholar
Bern, Z., Davies, S., Dennen, T., Smirnov, A. V., and Smirnov, V. A., “The ultraviolet properties of N = 4 supergravity at four loops,” Phys. Rev. Lett. 111, 231302 (2013) [arXiv:1309.2498 [hep-th]].10.1103/PhysRevLett.111.231302CrossRefGoogle Scholar
Bern, Z., Dixon, L. J., Dunbar, D. C., Perelstein, M., and Rozowsky, J. S., “On the relationship between Yang–Mills theory and gravity and its implication for ultraviolet divergences,” Nucl. Phys. B 530, 401 (1998) [hep-th/9802162].10.1016/S0550-3213(98)00420-9CrossRefGoogle Scholar
Dunbar, D. C., Julia, B., Seminara, D., and Trigiante, M., “Counterterms in type I supergravities,” JHEP 0001, 046 (2000) [hep-th/9911158].Google Scholar
Bern, Z., Davies, S., Dennen, T., and Y.-t. Huang, “Ultraviolet cancellations in halfmaximal supergravity as a consequence of the double-copy structure,” Phys. Rev. D 86, 105014 (2012) [arXiv:1209.2472 [hep-th]].10.1103/PhysRevD.86.105014CrossRefGoogle Scholar
Bern, Z., Davies, S., Dennen, T., and Y.-t. Huang, “Absence of three-loop four-point divergences in N = 4 supergravity,” Phys. Rev. Lett. 108, 201301 (2012) [arXiv:1202.3423 [hep-th]];10.1103/PhysRevLett.108.201301CrossRefGoogle ScholarPubMed
Fischler, M., “Finiteness calculations for O(4) through O(8) extended supergravity and O(4) supergravity coupled to selfdual O(4) matter,” Phys. Rev. D 20, 396 (1979).10.1103/PhysRevD.20.396CrossRefGoogle Scholar
Bern, Z., Davies, S., and Dennen, T., “The ultraviolet structure of half-maximal supergravity with matter multiplets at two and three loops,” [arXiv:1305.4876 [hep-th]].Google Scholar
Bossard, G., Howe, P. S., and Stelle, K. S., “Invariants and divergences in half-maximal supergravity theories,” [arXiv:1304.7753 [hep-th]].Google Scholar
Vaman, D. and Yao, Y.-P., “Constraints and generalized gauge transformations on tree-level gluon and graviton amplitudes,” JHEP 1011, 028 (2010) [arXiv:1007.3475 [hep-th]].Google Scholar
Boels, R. H. and Isermann, R. S., “On powercounting in perturbative quantum gravity theories through color-kinematic duality,” JHEP 1306, 017 (2013) [arXiv:1212.3473].Google Scholar
Bern, Z., Dennen, T., Y.-t. Huang, and Kiermaier, M., “Gravity as the square of gauge theory,” Phys. Rev. D 82, 065003 (2010) [arXiv:1004.0693 [hep-th]].10.1103/PhysRevD.82.065003CrossRefGoogle Scholar
Kiermaier, M., Talk at Amplitudes 2010, May 2010 at QMUL, London, UK. http://www.strings.ph.qmul.ac.uk/∼theory/Amplitudes2010/Google Scholar
Bjerrum-Bohr, N. E. J., Damgaard, P. H., Sondergaard, T., and Vanhove, P., “The momen-tum kernel of gauge and gravity theories,” JHEP 1101, 001 (2011) [arXiv:1010.3933 [hep-th]].Google Scholar
Mafra, C. R., Schlotterer, O., and Stieberger, S., “Explicit BCJ numerators from pure spinors,” JHEP 1107, 092 (2011) [arXiv:1104.5224 [hep-th]]Google ScholarGoogle Scholar
Bjerrum-Bohr, N. E. J., Damgaard, P. H., and Vanhove, P., “Minimal basis for gauge theory amplitudes,” Phys. Rev. Lett. 103, 161602 (2009) [0907.1425 [hep-th]]10.1103/PhysRevLett.103.161602Google ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Henry Tye, S. H. and Zhang, Y., “Dual identities inside the gluon and the graviton scattering amplitudes,” JHEP 1006, 071 (2010) [Erratum-ibid. 1104, 114 (2011)] [arXiv:1003.1732 [hep-th]].Google Scholar
Feng, B., Huang, R., and Jia, Y., “Gauge amplitude identities by on-shell recursion relation in s-matrix program,” Phys. Lett. B 695, 350 (2011) [arXiv:1004.3417 [hepth]].10.1016/j.physletb.2010.11.011CrossRefGoogle Scholar
Cachazo, F., “Fundamental BCJ relation in N = 4 SYM from the connected formulation,” [arXiv:1206.5970 [hep-th]].Google Scholar
Bjerrum-Bohr, N. E. J., Damgaard, P. H., Monteiro, R., and O’Connell, D., “Algebras for amplitudes,” JHEP 1206, 061 (2012) [arXiv:1203.0944 [hep-th]].Google Scholar
Monteiro, R. and O’Connell, D., “The kinematic algebra from the self-dual sector,” JHEP 1107, 007 (2011) [arXiv:1105.2565 [hep-th]].Google Scholar
Tolotti, M. and Weinzierl, S., “Construction of an effective Yang–Mills Lagrangian with manifest BCJ duality,” [arXiv:1306.2975 [hep-th]].Google Scholar
Bern, Z., Carrasco, J. J. M., and Johansson, H., “Perturbative quantum gravity as a double copy of gauge theory,” Phys. Rev. Lett. 105, 061602 (2010) [arXiv:1004.0476 [hep-th]].10.1103/PhysRevLett.105.061602CrossRefGoogle ScholarPubMed
Carrasco, J. J. and Johansson, H., “Five-point amplitudes in N = 4 super-Yang–Mills theory and N = 8 supergravity,” Phys. Rev. D 85, 025006 (2012) [arXiv:1106.4711 [hep-th]].10.1103/PhysRevD.85.025006CrossRefGoogle Scholar
Bjerrum-Bohr, N. E. J., Dennen, T., Monteiro, R., and O’Connell, D., “Integrand oxidation and one-loop colour-dual numerators in N = 4 gauge theory,” [arXiv:1303.2913 [hep-th]].Google Scholar
Boels, R. H., Isermann, R. S., Monteiro, R., and O’Connell, D., “Colour-kinematics duality for one-loop rational amplitudes,” JHEP 1304, 107 (2013) [arXiv:1301.4165 [hep-th]].Google Scholar
Carrasco, J. J. M., Chiodaroli, M., Günaydin, M., and Roiban, R., “One-loop four-point amplitudes in pure and matter-coupled N ≤ 4 supergravity,” JHEP 1303, 056 (2013) [arXiv:1212.1146 [hep-th]].Google Scholar
Chiodaroli, M., Jin, Q., and Roiban, R., “Color/kinematics duality for general abelian orbifolds of N = 4 super Yang–Mills theory,” JHEP 1401, 152 (2014) [arXiv:1311.3600 [hep-th]].Google Scholar
Nohle, J., “Color-kinematics duality in one-loop four-gluon amplitudes with matter,” [arXiv:1309.7416 [hep-th]].Google Scholar
Bern, Z., Boucher-Veronneau, C., and Johansson, H., “N ≥ 4 supergravity amplitudes from gauge theory at one loop,” Phys. Rev. D 84, 105035 (2011) [arXiv:1107.1935 [hep-th]]10.1103/PhysRevD.84.105035Google ScholarGoogle Scholar
Grisaru, M. T. and Siegel, W., “Supergraphity. 2. Manifestly covariant rules and higher loop finiteness,” Nucl. Phys. B 201, 292 (1982) [Erratum-ibid. B 206, 496 (1982)].Google Scholar
Ferrara, S., Kallosh, R., and Van Proeyen, A., “Conjecture on hidden superconformal symmetry of N = 4 supergravity,” Phys. Rev. D 87, 025004 (2013) [arXiv:1209.0418 [hep-th]].10.1103/PhysRevD.87.025004CrossRefGoogle Scholar
Broedel, J. and Dixon, L. J., “Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators,” JHEP 1210, 091 (2012) [arXiv:1208.0876 [hep-th]].Google Scholar
Boels, R. H., Kniehl, B. A., Tarasov, O. V., and Yang, G., “Color-kinematic duality for form factors,” JHEP 1302, 063 (2013) [arXiv:1211.7028 [hep-th]];Google Scholar
Bargheer, T., He, S., and McLoughlin, T., “New relations for three-dimensional supersymmetric scattering amplitudes,” Phys. Rev. Lett. 108, 231601 (2012) [arXiv:1203.0562 [hep-th]].10.1103/PhysRevLett.108.231601CrossRefGoogle ScholarPubMed
Huang, Y.-t. and Johansson, H., “Equivalent D = 3 supergravity amplitudes from double copies of three-algebra and two-algebra gauge theories,” [arXiv:1210.2255 [hep-th]].Google Scholar
Zee, A., “Quantum field theory in a nutshell,” Princeton, USA: Princeton University Press (2010).Google Scholar
Schwartz, M. D., Quantum Field Theory and the Standard Model, Cambridge, UK: Cambridge University Press (2013).10.1017/9781139540940CrossRefGoogle Scholar
Henn, J. M. and Plefka, J. C., “Scattering amplitudes in gauge theories,” Lecture Notes in Physics 883 Heidelbera: Springer (2014).Google Scholar
Wolf, M., “A first course on twistors, integrability and gluon scattering amplitudes,” J. Phys. A 43, 393001 (2010) [arXiv:1001.3871 [hep-th]].10.1088/1751-8113/43/39/393001CrossRefGoogle Scholar
Bern, Z., Dixon, L. J., and Kosower, D. A., “On-shell methods in perturbative QCD,” Annals Phys. 322, 1587 (2007) [arXiv:0704.2798 [hep-ph]].10.1016/j.aop.2007.04.014CrossRefGoogle Scholar
Peskin, M. E., “Simplifying multi-jet QCD computation,” [arXiv:1101.2414 [hep-ph]].Google Scholar
Donoghue, J. F., “Introduction to the effective field theory description of gravity,” gr-qc/9512024.Google Scholar
Dixon, L. J., “Ultraviolet behavior of N = 8 supergravity,” [arXiv:1005.2703 [hep-th]].Google Scholar
Bern, Z., Gondolo, P., and Perelstein, M., “Neutralino annihilation into two photons,” Phys. Lett. B 411, 86 (1997) [hep-ph/9706538]10.1016/S0370-2693(97)00990-8Google ScholarGoogle ScholarGoogle Scholar
Bidder, S. J., Bjerrum-Bohr, N. E. J., Dunbar, D. C., and Perkins, W. B., “One-loop gluon scattering amplitudes in theories with N < 4 supersymmetries,” Phys. Lett. B 612, 75 (2005) [hep-th/0502028].10.1016/j.physletb.2005.02.045CrossRefGoogle Scholar
Britto, R., Buchbinder, E., Cachazo, F., and Feng, B., “One-loop amplitudes of gluons in SQCD,” Phys. Rev. D 72, 065012 (2005) [hep-ph/0503132].10.1103/PhysRevD.72.065012CrossRefGoogle Scholar
Lal, S. and Raju, S., “Rational terms in theories with matter,” JHEP 1008, 022 (2010) [arXiv:1003.5264 [hep-th]].Google Scholar
Dittmaier, S., “Weyl-van der Waerden formalism for helicity amplitudes of massive particles,” Phys. Rev. D 59, 016007 (1998) [hep-ph/9805445].10.1103/PhysRevD.59.016007CrossRefGoogle Scholar
Boels, R. and Schwinn, C., “CSW rules for massive matter legs and glue loops,” Nucl. Phys. Proc. Suppl. 183, 137 (2008) [arXiv:0805.4577 [hep-th]].10.1016/j.nuclphysbps.2008.09.094CrossRefGoogle Scholar
Boels, R. H., “No triangles on the moduli space of maximally supersymmetric gauge theory,” JHEP 1005, 046 (2010) [arXiv:1003.2989 [hep-th]].Google Scholar
Ferrario, P., Rodrigo, G., and Talavera, P., “Compact multigluonic scattering amplitudes with heavy scalars and fermions,” Phys. Rev. Lett. 96, 182001 (2006) [hep-th/0602043].10.1103/PhysRevLett.96.182001CrossRefGoogle ScholarPubMed
Forde, D. and Kosower, D. A., “All-multiplicity amplitudes with massive scalars,” Phys. Rev. D 73, 065007 (2006) [hep-th/0507292].10.1103/PhysRevD.73.065007CrossRefGoogle Scholar
Rodrigo, G., “Multigluonic scattering amplitudes of heavy quarks,” JHEP 0509, 079 (2005) [hep-ph/0508138].Google Scholar
Cheung, C., O’Connell, D., and Wecht, B., “BCFW recursion relations and string theory,” JHEP 1009, 052 (2010) [arXiv:1002.4674 [hep-th]].Google Scholar
Boels, R. H., Marmiroli, D., and Obers, N. A., “On-shell recursion in string theory,” JHEP 1010, 034 (2010) [arXiv:1002.5029 [hep-th]].Google Scholar
Kampf, K., Novotny, J., and Trnka, J., “Recursion relations for tree-level amplitudes in the SU(N) non-linear sigma model,” Phys. Rev. D 87, 081701 (2013) [arXiv:1212.5224 [hep-th]].10.1103/PhysRevD.87.081701CrossRefGoogle Scholar
Bern, Z., Dixon, L. J., and Kosower, D. A., “The last of the finite loop amplitudes in QCD,” Phys. Rev. D 72, 125003 (2005) [hep-ph/0505055].10.1103/PhysRevD.72.125003CrossRefGoogle Scholar
Feng, B. and Luo, M., “An introduction to on-shell recursion relations,” [arXiv:1111.5759 [hep-th]].Google Scholar
Drummond, J. M., Korchemsky, G. P., and Sokatchev, E., “Conformal properties of four-gluon planar amplitudes and Wilson loops,” Nucl. Phys. B 795, 385 (2008) [arXiv:0707.0243 [hep-th]].Google Scholar
Berkovits, N. and Maldacena, J., “Fermionic T-duality, dual superconformal symmetry, and the amplitude/Wilson loop connection,” JHEP 0809, 062 (2008) [arXiv:0807.3196 [hep-th]].Google Scholar
Beisert, N., Ricci, R., Tseytlin, A. A., and Wolf, M., “Dual superconformal symmetry from AdS(5) x S∗∗5 superstring integrability,” Phys. Rev. D 78, 126004 (2008) [arXiv:0807.3228 [hep-th]].10.1103/PhysRevD.78.126004CrossRefGoogle Scholar
Brandhuber, A., Heslop, P., and Travaglini, G., “MHV amplitudes in N = 4 super Yang–Mills and Wilson loops,” Nucl. Phys. B 794, 231 (2008) [arXiv:0707.1153 [hep-th]].10.1016/j.nuclphysb.2007.11.002CrossRefGoogle Scholar
Mason, L. J. and Skinner, D., “The complete planar S-matrix of N = 4 SYM as a Wilson loop in twistor space,” JHEP 1012, 018 (2010) [arXiv:1009.2225 [hep-th]].Google Scholar
Caron-Huot, S., “Notes on the scattering amplitude / Wilson loop duality,” JHEP 1107, 058 (2011) [arXiv:1010.1167 [hep-th]].Google Scholar
Eden, B., Heslop, P., Korchemsky, G. P., and Sokatchev, E., “The super-correlator/superamplitude duality: Part I,” Nucl. Phys. B 869, 329 (2013) [arXiv:1103.3714 [hep-th]]Google ScholarGoogle Scholar
Alday, L. F., Eden, B., Korchemsky, G. P., Maldacena, J., and Sokatchev, E., “From correlation functions to Wilson loops,” JHEP 1109, 123 (2011) [arXiv:1007.3243 [hep-th]].Google Scholar
Adamo, T., Bullimore, M., Mason, L., and Skinner, D., “A proof of the supersymmetric correlation function / Wilson loop correspondence,” JHEP 1108, 076 (2011) [arXiv:1103.4119 [hep-th]].Google Scholar
Alday, L. F. and Roiban, R., “Scattering amplitudes, Wilson loops and the string/gauge theory correspondence,” Phys. Rept. 468, 153 (2008) [arXiv:0807.1889 [hep-th]].10.1016/j.physrep.2008.08.002CrossRefGoogle Scholar
Schabinger, R. M., “One-loop N = 4 super Yang–Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops,” J. Phys. A 44, 454007 (2011) [arXiv:1104.3873 [hep-th]].10.1088/1751-8113/44/45/454007CrossRefGoogle Scholar
Henn, J. M., “Duality between Wilson loops and gluon amplitudes,” Fortsch. Phys. 57, 729 (2009) [arXiv:0903.0522 [hep-th]].10.1002/prop.200900048CrossRefGoogle Scholar
Adamo, T., Bullimore, M., Mason, L., and Skinner, D., “Scattering amplitudes and Wilson loops in twistor space,” J. Phys. A 44, 454008 (2011) [arXiv:1104.2890 [hep-th]].10.1088/1751-8113/44/45/454008CrossRefGoogle Scholar
Alday, L. F., Gaiotto, D., Maldacena, J., Sever, A., and Vieira, P., “An operator product expansion for polygonal null Wilson loops,” JHEP 1104, 088 (2011) [arXiv:1006.2788 [hep-th]].Google Scholar
Basso, B., Sever, A., and Vieira, P., “Space-time S-matrix and flux-tube S-matrix at finite coupling,” Phys. Rev. Lett. 111, 091602 (2013) [arXiv:1303.1396 [hep-th]].10.1103/PhysRevLett.111.091602CrossRefGoogle Scholar
Basso, B., Sever, A., and Vieira, P., “Space-time S-matrix and flux tube S-matrix II. Extracting and matching data,” JHEP 1401, 008 (2014) [arXiv:1306.2058 [hep-th]].Google Scholar
Basso, B., Sever, A., and Vieira, P., “Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions,” [arXiv:1402.3307 [hep-th]].Google Scholar
Dixon, L. J., Drummond, J. M., von Hippel, M., and Pennington, J., “Hexagon functions and the three-loop remainder function,” JHEP 1312, 049 (2013) [arXiv:1308.2276 [hep-th]].Google Scholar
Dixon, L. J., Drummond, J. M., Duhr, C., and Pennington, J., “The four-loop remainder function and multi-Regge behavior at NNLLA in planar N = 4 super-Yang–Mills theory,” [arXiv:1402.3300 [hep-th]].Google Scholar
Penrose, R. and Rindler, W., Spinors and Space-Time, vol. 2, Cambridge: Cambridge University Press (1986).10.1017/CBO9780511524486CrossRefGoogle Scholar
Ward, R. and Wells, R., Twistor Geometry and Field Theory, Cambridge: Cambridge University Press (1990).10.1017/CBO9780511524493CrossRefGoogle Scholar
Huggett, S. and Tod, P., An Introduction to Twistor Theory, Student Texts 4, London: London Mathematical Society (1985).Google Scholar
Cachazo, F. and Svrcek, P., “Lectures on twistor strings and perturbative Yang–Mills theory,” PoS RTN 2005, 004 (2005) [hep-th/0504194].Google Scholar
Accessibility standard: Unknown
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
Accessibility compliance for the PDF of this book is currently unknown
and may be updated in the future.
You have
Access
Open access