[1] M. L., Mangano and S. J., Parke, “Multiparton amplitudes in gauge theories,”Phys. Rept. 200, 301 (1991) [hep-th/0509223].
[2] M., Srednicki, Quantum Field Theory, Cambridge, UK: Cambridge University Press (2007).
[3] L. J., Dixon, “Calculating scattering amplitudes efficiently,” In Boulder 1995, QCD and beyond, 539–582 [hep-ph/9601359].
[4] L. J., Dixon, “Scattering amplitudes: the most perfect microscopic structures in the universe,”J. Phys. A 44, 454001 (2011) [arXiv:1105.0771 [hep-th]].
[5] S. J., Parke and T. R., Taylor, “An amplitude for n gluon scattering,”Phys. Rev. Lett. 56, 2459 (1986).
[6] K., Kampf, J., Novotny, and J., Trnka, “Tree-level amplitudes in the nonlinear sigma model,”JHEP 1305, 032 (2013) [arXiv:1304.3048 [hep-th]].
[7] R., Kleiss and H., Kuijf, “Multi-gluon cross-sections and five jet production at hadron colliders,”Nucl. Phys. B 312, 616 (1989).
[8] V., Del Duca, L. J., Dixon, and F., Maltoni, “New color decompositions for gauge amplitudes at tree and loop level,”Nucl. Phys. B 571, 51 (2000) [hep-ph/9910563].
[9] Z., Bern, J. J. M., Carrasco, and H., Johansson, “New relations for gauge-theory amplitudes,”Phys. Rev. D 78, 085011 (2008) [arXiv:0805.3993 [hep-ph]].
[10] C. F., Berger, V., Del Duca, and L. J., Dixon, “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];
S. D., Badger, E. W. N., Glover, and K., Risager, “One-loop phi-MHV amplitudes using the unitarity bootstrap,”JHEP 0707, 066 (2007) [arXiv:0704.3914 [hep-ph]];
L. J., Dixon and Y., Sofianatos, “Analytic one-loop amplitudes for a Higgs boson plus four partons,”JHEP 0908, 058 (2009) [arXiv:0906.0008 [hep-ph]];
S., Badger, E. W., Nigel Glover, P., Mastrolia, and C., Williams, “One-loop Higgs plus four gluon amplitudes: Full analytic results,”JHEP 1001, 036 (2010) [arXiv:0909.4475 [hep-ph]].
[11] L. J., Dixon, “A brief introduction to modern amplitude methods,” [arXiv:1310.5353 [hep-ph]].
[12] F. A., Berends and W. T., Giele, “Recursive calculations for processes with n gluons,”Nucl. Phys. B 306, 759 (1988).
F. A., Berends, W. T., Giele, and H., Kuijf, “Exact and approximate expressions for multi-gluon scattering,”Nucl. Phys. B 333, 120 (1990).
[13] R., Britto, F., Cachazo, and B., Feng, “New recursion relations for tree amplitudes of gluons,”Nucl. Phys. B 715, 499 (2005) [hep-th/0412308].
[14] R., Britto, F., Cachazo, B., Feng, and E., Witten, “Direct proof of tree-level recursion relation in Yang–Mills theory,”Phys. Rev. Lett. 94, 181602 (2005) [hep-th/0501052].
[15] F., Cachazo, P., Svrcek, and E., Witten, “MHV vertices and tree amplitudes in gauge theory,”JHEP 0409, 006 (2004) [hep-th/0403047].
[16] B., Feng, J., Wang, Y., Wang, and Z., Zhang, “BCFW recursion relation with nonzero boundary contribution,”JHEP 1001, 019 (2010) [arXiv:0911.0301 [hep-th]].
[17] E., Conde and S., Rajabi, “The twelve-graviton next-to-MHV amplitude from Risager's construction,”JHEP 1209, 120 (2012) [arXiv:1205.3500 [hep-th]].
[18] N., Arkani-Hamed and J., Kaplan, “On tree amplitudes in gauge theory and gravity,”JHEP 0804, 076 (2008) [arXiv:0801.2385 [hep-th]].
[19] C., Cheung, “On-shell recursion relations for generic theories,”JHEP 1003, 098 (2010) [arXiv:0808.0504 [hep-th]].
[20] P., Benincasa, C., Boucher-Veronneau, and F., Cachazo, “Taming tree amplitudes in general relativity,”JHEP 0711, 057 (2007) [hep-th/0702032 [HEP-TH]].
[21] H., Kawai, D. C., Lewellen, and S. H. H., Tye, “A relation between tree amplitudes of closed and open strings,”Nucl. Phys. B 269, 1 (1986).
[22] S., Sannan, “Gravity as the limit of the type II superstring theory,”Phys. Rev. D 34, 1749 (1986).
[23] N., Arkani-Hamed, F., Cachazo, C., Cheung, and J., Kaplan, “A duality for the S matrix,”JHEP 1003, 020 (2010) [arXiv:0907.5418 [hep-th]].
[24] A., Hodges, “Eliminating spurious poles from gauge-theoretic amplitudes,”JHEP 1305, 135 (2013) [arXiv:0905.1473 [hep-th]].
[25] M., Spradlin, A., Volovich, and C., Wen, “Three applications of a bonus relation for gravity amplitudes,”Phys. Lett. B 674, 69 (2009) [arXiv:0812.4767 [hep-th]].
[26] T., Cohen, H., Elvang, and M., Kiermaier, “On-shell constructibility of tree amplitudes in general field theories,”JHEP 1104, 053 (2011) [arXiv:1010.0257 [hep-th]].
[27] H., Elvang, D. Z., Freedman, and M., Kiermaier, “Recursion relations, generating functions, and unitarity sums in N = 4 SYM theory,”JHEP 0904, 009 (2009) [arXiv:0808.1720 [hep-th]].
[28] K., Risager, “A direct proof of the CSW rules,”JHEP 0512, 003 (2005) [hep-th/ 0508206].
[29] H., Elvang, D. Z., Freedman, and M., Kiermaier, “Proof of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory,”JHEP 0906, 068 (2009) [arXiv:0811.3624 [hep-th]].
[30] L. J., Dixon, E. W. N., Glover, and V. V., Khoze, “MHV rules for Higgs plus multi-gluon amplitudes,”JHEP 0412, 015 (2004) [hep-th/0411092].
[31] S. D., Badger, E. W. N., Glover, and V. V., Khoze, “MHV rules for Higgs plus multi-parton amplitudes,”JHEP 0503, 023 (2005) [hep-th/0412275].
[32] A., Brandhuber, B., Spence, and G., Travaglini, “Tree-level formalism,”J. Phys. A 44, 454002 (2011) [arXiv:1103.3477 [hep-th]].
[33] A., Gorsky and A., Rosly, “From Yang–Mills Lagrangian to MHV diagrams,”JHEP 0601, 101 (2006) [hep-th/0510111];
P., Mansfield, “The Lagrangian origin of MHV rules,”JHEP 0603, 037 (2006) [hep-th/0511264];
J. H., Ettle and T. R., Morris, “Structure of the MHV-rules Lagrangian,”JHEP 0608, 003 (2006) [hep-th/0605121];
J. H., Ettle, C.-H., Fu, J. P., Fudger, P. R. W., Mansfield, and T. R., Morris, “S-matrix equivalence theorem evasion and dimensional regularisation with the canonical MHV Lagrangian,”JHEP 0705, 011 (2007) [hep-th/0703286];
H., Feng and Y.-t., Huang, “MHV Lagrangian for N = 4 super Yang–Mills,”JHEP 0904, 047 (2009) [hep-th/0611164].
[34] R., Boels, L. J., Mason, and D., Skinner, “From twistor actions to MHV diagrams,”Phys. Lett. B 648, 90 (2007) [hep-th/0702035].
[35] N. E. J., Bjerrum-Bohr, D. C., Dunbar, H., Ita, W. B., Perkins, and K., Risager, “MHV-vertices for gravity amplitudes,”JHEP 0601, 009 (2006) [hep-th/0509016].
[36] M., Bianchi, H., Elvang, and D. Z., Freedman, “Generating tree amplitudes in N = 4 SYM and N = 8 SG,”JHEP 0809, 063 (2008) [arXiv:0805.0757 [hep-th]].
[37] J., Wess and J., Bagger, Supersymmetry and Supergravity, Princeton, USA: University Press (1992).
[38] M. T., Grisaru and H. N., Pendleton, “Some properties of scattering amplitudes in supersymmetric theories,”Nucl. Phys. B 124, 81 (1977);
M. T., Grisaru, H. N., Pendleton, and P., van Nieuwenhuizen, “Supergravity and the S matrix,”Phys. Rev. D 15, 996 (1977).
[39] D. Z., Freedman and A., Van Proeyen, Supergravity, Cambridge, UK: Cambridge University Press (2012).
[40] L., Brink, J. H., Schwarz, and J., Scherk, “Supersymmetric Yang–Mills theories,”Nucl. Phys. B 121, 77 (1977).
[41] A., Ferber, “Supertwistors and conformal supersymmetry,”Nucl. Phys. B 132, 55 (1978).
[42] H., Elvang, D. Z., Freedman, and M., Kiermaier, “Solution to the Ward identities for superamplitudes,”JHEP 1010, 103 (2010) [arXiv:0911.3169 [hep-th]].
[43] H., Elvang, D. Z., Freedman, and M., Kiermaier, “SUSY Ward identities, super-amplitudes, and counterterms,”J. Phys. A 44, 454009 (2011) [arXiv:1012.3401 [hep-th]].
[44] M., Kiermaier and S. G., Naculich, “A super MHV vertex expansion for N = 4SYM theory,”JHEP 0905, 072 (2009) [arXiv:0903.0377 [hep-th]].
[45] N., Arkani-Hamed, “What is the simplest QFT?,” talk given at the Paris Workshop Wonders of Gauge Theory and Supergravity, 24 June 2008.
[46] A., Brandhuber, P., Heslop, and G., Travaglini, “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]].
[47] N., Arkani-Hamed, F., Cachazo, and J., Kaplan, “What is the simplest quantum field theory?,”JHEP 1009, 016 (2010) [arXiv:0808.1446 [hep-th]].
[48] Z., Bern, J. J. M., Carrasco, H., Ita, H., Johansson, and R., Roiban, “On the structure of supersymmetric sums in multi-loop unitarity cuts,”Phys.Rev.D 80, 065029 (2009) [arXiv:0903.5348 [hep-th]].
[49] J. M., Drummond and J. M., Henn, “All tree-level amplitudes in N = 4SYM,”JHEP 0904, 018 (2009) [arXiv:0808.2475 [hep-th]].
[50] J. M., Drummond, J., Henn, G. P., Korchemsky, and E., Sokatchev, “Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang–Mills theory,”Nucl. Phys. B 828, 317 (2010) [arXiv:0807.1095 [hep-th]].
[51] J. M., Drummond, M., Spradlin, A., Volovich, and C., Wen, “Tree-level amplitudes in N = 8 supergravity,”Phys. Rev. D 79, 105018 (2009) [arXiv:0901.2363 [hep-th]].
[52] J. M., Drummond, “Hidden simplicity of gauge theory amplitudes,”Class. Quant. Grav. 27, 214001 (2010) [arXiv:1010.2418 [hep-th]].
[53] R., Penrose, “Twistor algebra,”J. Math. Phys. 8, 345 (1967).
[54] E., Witten, “Perturbative gauge theory as a string theory in twistor space,”Commun. Math. Phys. 252, 189 (2004) [hep-th/0312171].
[55] P. A. M., Dirac, “Wave equations in conformal space,”Annals Math. 37, 429 (1936).
[56] W., Siegel, “Embedding versus 6D twistors,” [arXiv:1204.5679 [hep-th]].
[57] W., Siegel, “Fields,” [hep-th/9912205].
[58] J. M., Drummond, J., Henn, V. A., Smirnov, and E., Sokatchev, “Magic identities for conformal four-point integrals,”JHEP 0701, 064 (2007) [hep-th/0607160].
[59] J. M., Drummond, J. M., Henn, and J., Plefka, “Yangian symmetry of scattering amplitudes in N = 4 super Yang–Mills theory,”JHEP 0905, 046 (2009) [arXiv:0902.2987 [hep-th]].
[60] L. J., Mason and D., Skinner, “Dual superconformal invariance, momentum twistors and grassmannians,”JHEP 0911, 045 (2009) [arXiv:0909.0250 [hep-th]].
N., Arkani-Hamed, F., Cachazo, and C., Cheung, “The Grassmannian origin of dual superconformal invariance,”JHEP 10033, 036 (2010) [arXiv: 0909.0483 [hep-th]].
H., Elvang, Y.-t., Huang, C., Keeler, et al., “Grassmannians for scattering amplitudes in 4d N = 4 SYM and 3d ABJM,” 2014 [arXiv: 1410.0621 [hep.th]].
[61] R., Roiban, “Review of AdS/CFT integrability, Chapter V1: Scattering amplitudes – a brief introduction,”Lett. Math. Phys. 99, 455 (2012) [arXiv:1012.4001 [hep-th]].
[62] Lorenzo, Magnea, 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.pdf
[63] L. V., Bork, D. I., Kazakov, G. S., Vartanov, and A. V., Zhiboedov, “Construction of infrared finite observables in N = 4 super Yang–Mills theory,”Phys. Rev. D 81, 105028 (2010) [arXiv:0911.1617 [hep-th]].
[64] Z., Bern, G., Chalmers, L. J., Dixon, and D. A., Kosower, “One loop N gluon amplitudes with maximal helicity violation via collinear limits,”Phys. Rev. Lett. 72, 2134 (1994) [hep-ph/9312333].
[65] G., Mahlon, “Multi-gluon helicity amplitudes involving a quark loop,”Phys.Rev.D 49, 4438 (1994) [hep-ph/9312276].
[66] Z., Bern, L. J., Dixon, and D. A., Kosower, “Dimensionally regulated pentagon integrals,”Nucl. Phys. B 412, 751 (1994) [hep-ph/9306240].
[67] Z., Bern, L. J., Dixon, D. C., Dunbar, and D. A., Kosower, “One loop n point gauge theory amplitudes, unitarity and collinear limits,”Nucl. Phys. B 425, 217 (1994) [hep-ph/9403226];
Z., Bern, L. J., Dixon, D. C., Dunbar, and D. A., Kosower, “Fusing gauge theory tree amplitudes into loop amplitudes,”Nucl. Phys. B 435, 59 (1995) [hep-ph/9409265].
[68] J. J. M., Carrasco and H., Johansson, “Generic multiloop methods and application to N = 4 super-Yang–Mills,”J Phys. A 44, 454004 (2011) [arXiv:1103.3298 [hep-th]].
[69] Z., Bern and Y.-t., Huang, “Basics of generalized unitarity,”J. Phys. A 44, 454003 (2011) [arXiv:1103.1869 [hep-th]].
[70] H., Ita, “Susy theories and QCD: Numerical approaches,”J. Phys. A 44, 454005 (2011) [arXiv:1109.6527 [hep-th]].
[71] R., Britto, “Loop amplitudes in gauge theories: Modern analytic approaches,”J Phys. A 44, 454006 (2011) [arXiv:1012.4493 [hep-th]].
[72] W. L., van Neerven and J. A. M., Vermaseren, “Large loop integrals,”Phys. Lett. B 137, 241 (1984).
[73] Z., Bern, L. J., Dixon, and D. A., Kosower, “Dimensionally regulated one loop integrals,”Phys. Lett. B 302, 299 (1993) [Erratum-ibid. B318, 649 (1993)] [hep-ph/9212308].
[74] Z., Bern, L. J., Dixon, and D. A., Kosower, “Dimensionally regulated pentagon integrals,”Nucl. Phys. B 412, 751 (1994) [hep-ph/9306240].
[75] L. M., Brown and R. P., Feynman, “Radiative corrections to Compton scattering,”Phys. Rev. 85, 231 (1952);
G., 't Hooft and M. J. G., Veltman, “Scalar one loop integrals,”Nucl. Phys. B 153, 365 (1979).
[76] G., Passarino and M. J. G., Veltman, “One loop corrections for e+ e− annihilation into mu+ mu− in the Weinberg model,”Nucl. Phys. B 160, 151 (1979).
[77] R. K., Ellis, Z., Kunszt, K., Melnikov, and G., Zanderighi, “One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts,”Phys. Rept. 518, 141 (2012) [arXiv:1105.4319 [hep-ph]].
[78] H., Johansson, D. A., Kosower, and K. J., Larsen, “An overview of maximal unitarity at two loops,”PoSLL 2012, 066 (2012) [arXiv:1212.2132 [hep-th]].
[79] C., Anastasiou, R., Britto, B., Feng, Z., Kunszt, and P., Mastrolia, “D-dimensional unitarity cut method,”Phys. Lett. B 645, 213 (2007) [hep-ph/0609191];
R., Britto and B., Feng, “Integral coefficients for one-loop amplitudes,”JHEP 0802, 095 (2008) [0711.4284 [hep-ph]];
R., Britto and B., Feng, “Unitarity cuts with massive propagators and algebraic expressions for coefficients,”Phys. Rev. D 75, 105006 (2007) [hep-ph/0612089];
G., Ossola, C. G., Papadopoulos, and R., Pittau, “Reducing full one-loop amplitudes to scalar integrals at the integrand level,”Nucl. Phys. B 763, 147 (2007) [hep-ph/0609007];
R., Britto, B., Feng, and P., Mastrolia, “Closed-form decomposition of one-loop massive amplitudes,”Phys. Rev. D 78, 025031 (2008) [0803.1989 [hep-ph]];
D., Forde, “Direct extraction of one-loop integral coefficients,”Phys. Rev. D 75, 125019 (2007) [0704.1835 [hep-ph]];
[80] Z., Bern and A. G., Morgan, “Massive loop amplitudes from unitarity,”Nucl. Phys. B 467, 479 (1996) [hep-ph/9511336];
Z., Bern, L. J., Dixon, and D. A., Kosower, “Progress in one-loop QCD computations,”Ann. Rev. Nucl. Part. Sci. 46, 109 (1996) [hep-ph/9602280].
[81] S. D., Badger, “Direct extraction of one loop rational terms,”JHEP 0901, 049 (2009) [0806.4600 [hep-ph]].
[82] M. B., Green, J. H., Schwarz, and L., Brink, “N = 4 Yang-Mills and N = 8 supergravity as limits of string theories,”Nucl. Phys. B 198, 474 (1982).
[83] Z., Bern, N. E. J., Bjerrum-Bohr, and D. C., Dunbar, “Inherited twistor-space structure of gravity loop amplitudes,”JHEP 0505, 056 (2005) [hep-th/0501137];
N. E. J., Bjerrum-Bohr, D. C., Dunbar, H., Ita, W. B., Perkins, and K., Risager, “The no-triangle hypothesis for N = 8 supergravity,”JHEP 0612, 072 (2006) [hepth/0610043];
N. E. J., Bjerrum-Bohr and P., Vanhove, “Absence of triangles in maximal supergravity amplitudes,”JHEP 0810, 006 (2008) [arXiv:0805.3682 [hep-th]].
[84] Z., Bern, J. J., Carrasco, D., Forde, H., Ita, and H., Johansson, “Unexpected cancellations in gravity theories,”Phys. Rev. D 77, 025010 (2008) [arXiv:0707.1035 [hep-th]].
[85] S., Lal and S., Raju, “The next-to-simplest quantum field theories,”Phys. Rev. D 81, 105002 (2010) [arXiv:0910.0930 [hep-th]].
[86] D. C., Dunbar, J. H., Ettle, and W. B., Perkins, “Perturbative expansion of N < 8 supergravity,”Phys. Rev. D 83, 065015 (2011) [arXiv:1011.5378 [hep-th]].
[87] H., Elvang, Y.-t., Huang, and C., Peng, “On-shell superamplitudes in N < 4 SYM,”JHEP 1109, 031 (2011) [arXiv:1102.4843 [hep-th]].
[88] Y.-t., Huang, D. A., McGady, and C., Peng, “One-loop renormalization and the S-matrix,” [arXiv:1205.5606 [hep-th]].
[89] N., Marcus, “Composite anomalies in supergravity,”Phys. Lett. B 157, 383 (1985).
[90] P., di Vecchia, S., Ferrara, and L., Girardello, “Anomalies of hidden local chiral symmetries in sigma models and extended supergravities,”Phys. Lett. B 151, 199 (1985).
[91] J. M., Drummond, J., Henn, G. P., Korchemsky, and E., Sokatchev, “Generalized unitarity for N = 4 super-amplitudes,”Nucl. Phys. B 869, 452 (2013) [arXiv:0808.0491 [hep-th]].
[92] A., Brandhuber, P., Heslop, and G., Travaglini, “One-loop amplitudes in N = 4 super Yang–Mills and anomalous dual conformal symmetry,”JHEP 0908, 095 (2009) [arXiv:0905.4377 [hep-th]].
[93] H., Elvang, D. Z., Freedman, and M., Kiermaier, “Dual conformal symmetry of 1-loop NMHV amplitudes in N = 4 SYM theory,”JHEP 1003, 075 (2010) [arXiv:0905.4379 [hep-th]].
[94] G. P., Korchemsky and E., Sokatchev, “Symmetries and analytic properties of scattering amplitudes in N = 4 SYM theory,”Nucl. Phys. B 832, 1 (2010) [arXiv:0906.1737 [hep-th]].
[95] J., Gluza, K., Kajda, and D. A., Kosower, “Towards a basis for planar two-loop integrals,”Phys. Rev. D 83, 045012 (2011) [arXiv:1009.0472 [hep-th]].
[96] D. A., Kosower and K. J., Larsen, “Maximal unitarity at two loops,”Phys. Rev. D 85, 045017 (2012) [arXiv:1108.1180 [hep-th]];
H., Johansson, D. A., Kosower, and K. J., Larsen, “Two-loop maximal unitarity with external masses,”Phys. Rev. D 87, 025030 (2013) [arXiv:1208.1754 [hep-th]].
[97] S., Badger, H., Frellesvig, and Y., Zhang, “Hepta-cuts of two-loop scattering amplitudes,”JHEP 1204, 055 (2012) [arXiv:1202.2019 [hep-ph]].
[98] Y., Zhang, “Integrand-level reduction of loop amplitudes by computational algebraic geometry methods,”JHEP 1209, 042 (2012) [arXiv:1205.5707 [hep-ph]].
[99] M., Sgaard, “Global residues and two-loop hepta-cuts,”JHEP 1309, 116 (2013) [arXiv:1306.1496 [hep-th]].
[100] A. V., Smirnov and A. V., Petukhov, “The number of master integrals is finite,”Lett. Math. Phys. 97, 37 (2011) [arXiv:1004.4199 [hep-th]].
[101] C., Anastasiou, Z., Bern, L. J., Dixon, and D. A., Kosower, “Planar amplitudes in maximally supersymmetric Yang–Mills theory,”Phys. Rev. Lett. 91, 251602 (2003) [hep-th/0309040].
[102] Z., Bern, L. J., Dixon, and V. A., Smirnov, “Iteration of planar amplitudes in maximally supersymmetric Yang–Mills theory at three loops and beyond,”Phys. Rev. D 72, 085001 (2005) [hep-th/0505205].
[103] Z., Bern, J. S., Rozowsky, and B., Yan, “Two loop four gluon amplitudes in N = 4 super Yang–Mills,”Phys. Lett. B 401, 273 (1997) [hep-ph/9702424].
[104] Z., Bern, M., Czakon, D. A., Kosower, R., Roiban, and V. A., Smirnov, “Two-loop iteration of five-point N = 4 super-Yang–Mills amplitudes,”Phys. Rev. Lett. 97, 181601 (2006) [hep-th/0604074].
[105] F., Cachazo, M., Spradlin, and A., Volovich, “Iterative structure within the five-particle two-loop amplitude,”Phys. Rev. D 74, 045020 (2006) [hep-th/0602228].
[106] L. F., Alday and J., Maldacena, “Comments on gluon scattering amplitudes via AdS/CFT,”JHEP 0711, 068 (2007) [arXiv:0710.1060 [hep-th]].
[107] L. F., Alday and J. M., Maldacena, “Gluon scattering amplitudes at strong coupling,”JHEP 0706, 064 (2007) [arXiv:0705.0303 [hep-th]].
[108] Z., Bern, L. J., Dixon, D. A., Kosower, et al., “The two-loop six-gluonMHV amplitude in maximally supersymmetric Yang–Mills theory,”Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465 [hep-th]].
[109] F., Cachazo, M., Spradlin, and A., Volovich, “Leading singularities of the two-loop six-particle MHV amplitude,”Phys.Rev. D 78, 105022 (2008) [arXiv:0805.4832 [hep-th]].
[110] V., Del Duca, C., Duhr, and V. A., Smirnov, “An analytic result for the two-loop hexagon Wilson loop in N = 4SYM,”JHEP 1003, 099 (2010) [arXiv:0911.5332 [hep-ph]].
[111] V., Del Duca, C., Duhr, and V. A., Smirnov, “The two-loop hexagon Wilson loop in N = 4 SYM,”JHEP 1005, 084 (2010) [arXiv:1003.1702 [hep-th]].
[112] A. B., Goncharov, M., Spradlin, C., Vergu, and A., Volovich, “Classical polylogarithms for amplitudes and Wilson loops,”Phys. Rev. Lett. 105, 151605 (2010) [arXiv:1006.5703 [hep-th]].
[113] E. W., Nigel Glover and C., Williams, “One-loop gluonic amplitudes from single unitarity cuts,”JHEP 0812, 067 (2008) [0810.2964 [hep-th]];
I., Bierenbaum, S., Catani, P., Draggiotis, and G., Rodrigo, “A tree-loop duality relation at two loops and beyond,”JHEP 1010, 073 (2010) [arXiv:1007.0194 [hep-ph]];
H., Elvang, D. Z., Freedman, and M., Kiermaier, “Integrands for QCD rational terms and N = 4 SYM frommassive CSW rules,”JHEP 1206, 015 (2012) [arXiv:1111.0635 [hep-th]].
[114] S., Caron-Huot, “Loops and trees,”JHEP 1105, 080 (2011) [arXiv:1007.3224 [hep-ph]].
[115] N., Arkani-Hamed, J. L., Bourjaily, F., Cachazo, S., Caron-Huot, and J., Trnka, “The all-loop integrand for scattering amplitudes in planar N = 4 SYM,”JHEP 1101, 041 (2011) [arXiv:1008.2958 [hep-th]].
[116] R. H., Boels, “On BCFW shifts of integrands and integrals,”JHEP 1011, 113 (2010) [arXiv:1008.3101 [hep-th]].
[117] Z., Bern, J. J. M., Carrasco, H., Johansson, and D. A., Kosower, “Maximally supersymmetric planar Yang–Mills amplitudes at five loops,”Phys.Rev. D 76, 125020 (2007) [0705.1864 [hep-th]].
[118] R., Britto, F., Cachazo, and B., Feng, “Generalized unitarity and one-loop amplitudes in N = 4 super-Yang–Mills,”Nucl. Phys. B 725, 275 (2005) [hep-th/0412103];
E. I., Buchbinder and F., Cachazo, “Two-loop amplitudes of gluons and octa-cuts in N = 4 super Yang–Mills,”JHEP 0511, 036 (2005) [hep-th/0506126].
[119] N., Arkani-Hamed, J. L., Bourjaily, F., Cachazo, and J., Trnka, “Local integrals for planar scattering amplitudes,”JHEP 1206, 125 (2012) [arXiv:1012.6032 [hep-th]].
For extensions, see J. L., Bourjaily, S., Caron-Huot, and J., Trnka, “Dual-conformal regularization of infrared loop divergences and the chiral box expansion,” [arXiv:1303.4734 [hep-th]].
[120] N., Arkani-Hamed, J. L., Bourjaily, F., Cachazo, et al., “Scattering amplitudes and the positive Grassmannian,” [arXiv:1212.5605 [hep-th]].
[121] F., Cachazo, “Sharpening the leading singularity,” [arXiv:0803.1988 [hep-th]].
[122] J. M., Drummond and L., Ferro, “Yangians, Grassmannians and T-duality,”JHEP 1007, 027 (2010) [arXiv:1001.3348 [hep-th]].
[123] J. M., Drummond and L., Ferro, “The Yangian origin of the Grassmannian integral,”JHEP 1012, 010 (2010) [arXiv:1002.4622 [hep-th]];
G. P., Korchemsky and E., Sokatchev, “Superconformal invariants for scattering amplitudes in N = 4 SYM theory,”Nucl. Phys. B 839, 377 (2010) [arXiv:1002.4625 [hep-th]].
[124] R., Roiban, M., Spradlin, and A., Volovich, “On the tree level S matrix of Yang–Mills theory,”Phys. Rev. D 70, 026009 (2004) [hep-th/0403190].
[125] M., Spradlin and A., Volovich, “From twistor string theory to recursion relations,”Phys. Rev. D 80, 085022 (2009) [arXiv:0909.0229 [hep-th]].
[126] N., Arkani-Hamed, J., Bourjaily, F., Cachazo, and J., Trnka, “Unification of residues and Grassmannian dualities,”JHEP 1101, 049 (2011) [arXiv:0912.4912 [hep-th]].
[127] J. L., Bourjaily, J., Trnka, A., Volovich, and C., Wen, “The Grassmannian and the twistor string: Connecting all trees in N = 4 SYM,”JHEP 1101, 038 (2011) [arXiv:1006.1899 [hep-th]].
[128] M., Bullimore, L. J., Mason, and D., Skinner, “Twistor-strings, Grassmannians and leading singularities,”JHEP 1003, 070 (2010) [arXiv:0912.0539 [hep-th]].
[129] L., Dolan and P., Goddard, “Complete equivalence between gluon tree amplitudes in twistor string theory and in gauge theory,”JHEP 1206, 030 (2012) [arXiv:1111.0950 [hep-th]].
[130] N., Arkani-Hamed, J. L., Bourjaily, F., Cachazo, A., Hodges, and J., Trnka, “A note on polytopes for scattering amplitudes,”JHEP 1204, 081 (2012) [arXiv:1012.6030 [hep-th]].
[131] M., Bullimore, L. J., Mason, and D., Skinner, “MHV diagrams in momentum twistor space,”JHEP 1012, 032 (2010) [arXiv:1009.1854 [hep-th]].
[132] N., Arkani-Hamed and J., Trnka, “The amplituhedron,” [arXiv:1312.2007 [hep-th]];
N., Arkani-Hamed and J., Trnka, “Into the amplituhedron,” [arXiv:1312.7878 [hep-th]].
[133] L., Mason and D., Skinner, “Amplitudes at weak coupling as polytopes in AdS5,”J. Phys. A 44, 135401 (2011) [arXiv:1004.3498 [hep-th]].
[134] H., Nastase and H. J., Schnitzer, “Twistor and polytope interpretations for subleading color one-loop amplitudes,”Nucl. Phys. B 855, 901 (2012) [arXiv:1104.2752 [hep-th]].
[135] R., Boels, “Covariant representation theory of the Poincaré algebra and some of its extensions,”JHEP 1001, 010 (2010) [arXiv:0908.0738 [hep-th]].
[136] S., Caron-Huot and D., O'Connell, “Spinor helicity and dual conformal symmetry in ten dimensions,”JHEP 1108, 014 (2011) [arXiv:1010.5487 [hep-th]].
[137] R. H., Boels and D., O'Connell, “Simple superamplitudes in higher dimensions,”JHEP 1206, 163 (2012) [arXiv:1201.2653 [hep-th]].
[138] S., Davies, “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]].
[139] Z., Bern, J. J., Carrasco, T., Dennen, Y.-t., Huang, and H., Ita, “Generalized unitarity and six-dimensional helicity,”Phys. Rev. D 83, 085022 (2011) [arXiv:1010.0494 [hep-th]].
[140] N., Craig, H., Elvang, M., Kiermaier, and T., Slatyer, “Massive amplitudes on the Coulomb branch of N = 4SYM,”JHEP 1112, 097 (2011) [arXiv:1104.2050 [hep-th]].
[141] C., Cheung and D., O'Connell, “Amplitudes and spinor-helicity in six dimensions,”JHEP 0907, 075 (2009) [arXiv:0902.0981 [hep-th]].
[142] T., Dennen, Y.-t., Huang, and W., Siegel, “Supertwistor space for 6D maximal super Yang–Mills,”JHEP 1004, 127 (2010) [arXiv:0910.2688 [hep-th]].
[143] A., Brandhuber, D., Korres, D., Koschade, and G., Travaglini, “One-loop amplitudes in six-dimensional (1,1) theories from generalised unitarity,”JHEP 1102, 077 (2011) [arXiv:1010.1515 [hep-th]];
C., Saemann, R., Wimmer, and M., Wolf, “A twistor description of six-dimensional N = (1,1) super Yang–Mills theory,”JHEP 1205, 020 (2012) [arXiv:1201.6285 [hep-th]].
[144] T., Dennen and Y.-t., Huang, “Dual conformal properties of six-dimensional maximal super Yang–Mills amplitudes,”JHEP 1101, 140 (2011) [arXiv:1010.5874 [hep-th]].
[145] T., Chern, “Superconformal field theory in six dimensions and supertwistor,” [arXiv:0906.0657 [hep-th]];
M., Chiodaroli, M., Gunaydin, and R., Roiban, “Superconformalsymmetry, and maximal supergravity in various dimensions,”JHEP 1203, 093 (2012) [arXiv:1108.3085 [hep-th]];
L. J., Mason, R. A., Reid-Edwards, and A., Taghavi-Chabert, “Conformal field theories in six-dimensional twistor space,”J. Geom. Phys. 62, 2353 (2012) [arXiv:1111.2585 [hep-th]];
C., Saemann and M., Wolf, “On twistors and conformal field theories from six dimensions,”J. Math. Phys. 54, 013507 (2013) [arXiv:1111.2539 [hep-th]].
[146] B., Czech, Y.-t., Huang, and M., Rozali, “Amplitudes for multiple M5 branes,”JHEP 1210, 143 (2012) [arXiv:1110.2791 [hep-th]].
[147] C., Saemann and M., Wolf, “Non-Abelian tensor multiplet equations from twistor space,” [arXiv:1205.3108 [hep-th]].
[148] Y.-t., Huang and A. E., Lipstein, “Amplitudes of 3D and 6D maximal superconformal theories in supertwistor space,”JHEP 1010, 007 (2010) [arXiv:1004.4735 [hep-th]].
[149] L. F., Alday, J. M., Henn, J., Plefka, and T., Schuster, “Scattering into the fifth dimension of N = 4 super Yang–Mills,”JHEP 1001, 077 (2010) [arXiv:0908.0684 [hep-th]].
[150] A., Agarwal, N., Beisert, and T., McLoughlin, “Scattering in mass-deformed N ≥ 4 Chern–Simons models,”JHEP 0906, 045 (2009) [arXiv:0812.3367 [hep-th]].
[151] A., Gustavsson, “Algebraic structures on parallel M2-branes,”Nucl. Phys. B 811, 66 (2009) [arXiv:0709.1260 [hep-th]].
[152] J., Bagger and N., Lambert, “Gauge symmetry and supersymmetry of multiple M2-branes,”Phys.Rev. D 77, 065008 (2008) [arXiv:0711.0955 [hep-th]].
[153] M. A., Bandres, A. E., Lipstein, and J. H., Schwarz, “N = 8 superconformal Chern–Simons theories,”JHEP 0805, 025 (2008) [arXiv:0803.3242 [hep-th]].
[154] J., Gomis, G., Milanesi, and J. G., Russo, “Bagger-Lambert theory for general Lie algebras,”JHEP 0806, 075 (2008) [arXiv:0805.1012 [hep-th]].
[155] S., Benvenuti, D., Rodriguez-Gomez, E., Tonni, and H., Verlinde, “N = 8 superconformal gauge theories and M2 branes,”JHEP 0901, 078 (2009) [arXiv:0805.1087 [hep-th]].
[156] P. -M., Ho, Y., Imamura, and Y., Matsuo, “M2 to D2 revisited,”JHEP 0807, 003 (2008) [arXiv:0805.1202 [hep-th]].
[157] T., Bargheer, F., Loebbert, and C., Meneghelli, “Symmetries of tree-level scattering amplitudes in N = 6 superconformal Chern–Simons theory,”Phys. Rev. D 82, 045016 (2010) [arXiv:1003.6120 [hep-th]].
[158] O., Aharony, O., Bergman, D. L., Jafferis, and J., Maldacena, “N = 6 superconformal Chern–Simons-matter theories, M2-branes and their gravity duals,”JHEP 0810, 091 (2008) [arXiv:0806.1218 [hep-th]].
[159] M., Benna, I., Klebanov, T., Klose, and M., Smedback, “Superconformal Chern–Simons theories and AdS(4)/CFT(3) correspondence,”JHEP 0809, 072 (2008) [arXiv:0806.1519 [hep-th]].
[160] M. A., Bandres, A. E., Lipstein, and J. H., Schwarz, “Studies of the ABJM theory in a formulation with manifest SU(4) R-symmetry,”JHEP 0809, 027 (2008) [arXiv:0807.0880 [hep-th]].
[161] A., Gustavsson, “Selfdual strings and loop space Nahm equations,”JHEP 0804, 083 (2008) [arXiv:0802.3456 [hep-th]];
J., Bagger and N., Lambert, “Three-algebras and N = 6 Chern–Simons gauge theories,”Phys. Rev. D 79, 025002 (2009) [arXiv:0807.0163 [hep-th]].
[162] D., Gang, Y.-t., Huang, E., Koh, S., Lee, 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]].
[163] Y.-t., Huang and A. E., Lipstein, “Dual superconformal symmetry of N = 6 Chern–Simons theory,”JHEP 1011, 076 (2010) [arXiv:1008.0041 [hep-th]].
[164] T., Bargheer, N., Beisert, F., Loebbert, and T., McLoughlin, “Conformal anomaly for amplitudes in N = 6 superconformal Chern–Simons theory,”J. Phys. A 45, 475402 (2012) [arXiv:1204.4406 [hep-th]].
[165] M. S., Bianchi, M., Leoni, A., Mauri, S., Penati, and A., Santambrogio, “One loop amplitudes In ABJM,”JHEP 1207, 029 (2012) [arXiv:1204.4407 [hep-th]].
[166] A., Brandhuber, G., Travaglini, and C., Wen, “All one-loop amplitudes in N = 6 superconformal Chern–Simons theory,”JHEP 1210, 145 (2012) [arXiv:1207.6908 [hep-th]].
[167] W. -M., Chen and Y.-t., Huang, “Dualities for loop amplitudes of N = 6 Chern–Simons matter theory,”JHEP 1111, 057 (2011) [arXiv:1107.2710 [hep-th]];
[168] A., Brandhuber, G., Travaglini, and C., Wen, “A note on amplitudes in N = 6 superconformal Chern–Simons theory,”JHEP 1207, 160 (2012) [arXiv:1205.6705 [hep-th]].
[169] M. S., Bianchi, M., Leoni, A., Mauri, S., Penati, and A., Santambrogio, “Scattering amplitudes/Wilson loop duality in ABJM theory,”JHEP 1201, 056 (2012) [arXiv:1107.3139 [hep-th]].
[170] S., Caron-Huot and Y.-t., Huang, “The two-loop six-point amplitude in ABJM theory,”JHEP 1303, 075 (2013) [arXiv:1210.4226 [hep-th]].
[171] S., Lee, “Yangian invariant scattering amplitudes in supersymmetric Chern–Simons theory,”Phys. Rev. Lett. 105, 151603 (2010) [arXiv:1007.4772 [hep-th]].
[172] Y. -t., Huang, C., Wen, and D., Xie, “The positive orthogonal Grassmannian and loop amplitudes of ABJM,” [arXiv:1402.1479 [hep-th]].
[173] Y.-t., Huang and S., Lee, “A new integral formula for supersymmetric scattering amplitudes in three dimensions,”Phys. Rev. Lett. 109, 191601 (2012) [arXiv:1207.4851 [hep-th]].
[174] O. T., Engelund and R., Roiban, “A twistor string for the ABJ(M) theory,” [arXiv:1401.6242 [hep-th]].
[175] S., Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, USA: John Wiley & Sons (1972).
[176] R. M., Wald, General Relativity, Chicago, USA: University Press (1984).
[177] S. M., Carroll, Spacetime and Geometry: An Introduction to General Relativity, San Francisco, USA: Addison-Wesley (2004).
[178] H., Elvang and D. Z., Freedman, unpublished notes (2007).
[179] B. S., DeWitt, “Quantum theory of gravity. 2. The manifestly covariant theory,”Phys. Rev. 162, 1195 (1967);
B. S., DeWitt, “Quantum theory of gravity. 3. Applications of the covariant theory,”Phys. Rev. 162, 1239 (1967);
M. J. G., Veltman, “Quantum theory of gravitation,”Conf. Proc. C 7507281, 265 (1975).
[180] F. A., Berends, W. T., Giele, and H., Kuijf, “On relations between multi-gluon and multigraviton scattering,”Phys. Lett. B 211, 91 (1988).
[181] J., Bedford, A., Brandhuber, B. J., Spence, and G., Travaglini, “A recursion relation for gravity amplitudes,”Nucl. Phys. B 721, 98 (2005) [hep-th/0502146].
[182] H., Elvang and D. Z., Freedman, “Note on graviton MHV amplitudes,”JHEP 0805, 096 (2008) [arXiv:0710.1270 [hep-th]].
[183] D., Nguyen, M., Spradlin, A., Volovich, and C., Wen, “The tree formula for MHV graviton amplitudes,”JHEP 1007, 045 (2010) [arXiv:0907.2276 [hep-th]].
[184] Z., Bern, L. J., Dixon, M., Perelstein, and J. S., Rozowsky, “Multileg one loop gravity amplitudes from gauge theory,”Nucl. Phys. B 546, 423 (1999) [hep-th/9811140].
[185] Z., Bern and A. K., Grant, “Perturbative gravity from QCD amplitudes,”Phys. Lett. B 457, 23 (1999) [hep-th/9904026].
[186] Z., Bern, L. J., Dixon, D. C., Dunbar, et al., “On perturbative gravity and gauge theory,”Nucl. Phys. Proc. Suppl. 88, 194 (2000) [hep-th/0002078].
[187] W., Siegel, “Two vierbein formalism for string inspired axionic gravity,”Phys. Rev. D 47, 5453 (1993) [hep-th/9302036].
[188] Z., Bern, “Perturbative quantum gravity and its relation to gauge theory,”Living Rev. Rel 5, 5 (2002) [gr-qc/0206071].
[189] D. Z., Freedman, “Some beautiful equations of mathematical physics,” In ICTP (ed.): The Dirac Medals of the ICTP 199325–53, and CERN Geneva - TH.-7367 (94/07,rec.Sep.) [hep-th/9408175].
[190] S. J., Gates, M. T., Grisaru, M., Rocek, and W., Siegel, “Superspace or one thousand and one lessons in supersymmetry,”Front. Phys. 58, 1 (1983) [hep-th/0108200].
[191] B., de Wit and D. Z., Freedman, “On SO(8) extended supergravity,”Nucl. Phys. B 130, 105 (1977).
[192] E., Cremmer and B., Julia, “The N = 8 supergravity theory. 1. The Lagrangian,”Phys. Lett. B 80, 48 (1978);
E., Cremmer and B., Julia, “The SO(8) supergravity,”Nucl. Phys. B 159, 141 (1979).
[193] B., de Wit and H., Nicolai, “N = 8 supergravity,”Nucl. Phys. B 208, 323 (1982).
[194] A., Hodges, “A simple formula for gravitational MHV amplitudes,” [arXiv:1204.1930[hep-th]].
[195] F., Cachazo, L., Mason, and D., Skinner, “Gravity in twistor space and its Grassmannian formulation,” [arXiv:1207.4712 [hep-th]].
[196] S., He, “A link representation for gravity amplitudes,” [arXiv:1207.4064 [hep-th]].
[197] F., Cachazo and Y., Geyer, “A ‘twistor string’ inspired formula for tree-level scattering amplitudes in N = 8 SUGRA,” [arXiv:1206.6511 [hep-th]].
[198] D., Skinner, “Twistor strings for N = 8 supergravity,” [arXiv:1301.0868 [hep-th]].
[199] F., Cachazo, S., He, and E. Y., Yuan, “Scattering equations and KLT orthogonality,” [arXiv:1306.6575 [hep-th]].
[200] F., Cachazo, S., He, and E. Y., Yuan, “Scattering of massless particles in arbitrary dimension,” [arXiv:1307.2199 [hep-th]].
[201] S. L., Adler, “Consistency conditions on the strong interactions implied by a partially conserved axial vector current,”Phys. Rev. 137, B1022 (1965).
[202] S. R., Coleman, “Secret symmetry: An introduction to spontaneous symmetry breakdown and gauge fields,”Subnucl. Ser. 11, 139 (1975).
[203] M., Kiermaier, “The Coulomb-branch S-matrix from massless amplitudes,” [arXiv:1105.5385 [hep-th]].
[204] G. 't, Hooft and M. J. G., Veltman, “One loop divergencies in the theory of gravitation,”Annales Poincare Phys. Theor. A 20, 69 (1974).
[205] M. H., Goroff and A., Sagnotti, “Quantum gravity at two loops,”Phys. Lett. B 160, 81 (1985).
[206] A. E. M., van de Ven, “Two loop quantum gravity,”Nucl. Phys. B 378, 309 (1992).
[207] S., Deser and P., van Nieuwenhuizen, “One loop divergences of quantized Einstein–Maxwell fields,”Phys.Rev. D 10, 401 (1974).
[208] M. T., Grisaru, P., van Nieuwenhuizen, and J. A. M., Vermaseren, “One loop renor-malizability of pure supergravity and of Maxwell–Einstein theory in extended supergravity,”Phys. Rev. Lett. 37, 1662 (1976).
[209] M. T., Grisaru, “Two loop renormalizability of supergravity,”Phys. Lett. B 66, 75 (1977).
[210] E., Tomboulis, “On the two loop divergences of supersymmetric gravitation,”Phys. Lett. B 67, 417 (1977).
[211] S., Deser, J. H., Kay, and K. S., Stelle, “Renormalizability properties of supergravity,”Phys. Rev. Lett. 38, 527 (1977).
[212] Z., Bern, L. J., Dixon, and R., Roiban, “Is N = 8 supergravity ultraviolet finite?,”Phys. Lett. B 644, 265 (2007) [hep-th/0611086].
[213] Z., Bern, J. J., Carrasco, L. J., Dixon, et al., “Three-loop superfiniteness of N = 8 supergravity,”Phys. Rev. Lett. 98, 161303 (2007) [hep-th/0702112].
[214] Z., Bern, J. J. M., Carrasco, L. J., Dixon, H., Johansson, and R., Roiban, “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]].
[215] P. S., Howe and K. S., Stelle, “Supersymmetry counterterms revisited,”Phys. Lett. B 554, 190 (2003) [hep-th/0211279].
[216] Z., Bern, J. J., Carrasco, L. J., Dixon, H., Johansson, and R., Roiban, “The ultraviolet behavior of N = 8 supergravity at four loops,”Phys. Rev. Lett. 103, 081301 (2009) [arXiv:0905.2326 [hep-th]].
[217] Z., Bern, J. J. M., Carrasco, L. J., Dixon, H., Johansson, and R., Roiban, “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]].
[218] J., BjornssonandM. B., Green, “5 loops in 24/5 dimensions,”JHEP 1008, 132 (2010) [arXiv:1004.2692 [hep-th]].
[219] H., Elvang, D. Z., Freedman, and M., Kiermaier, “A simple approach to counterterms in N = 8 supergravity,”JHEP 1011, 016 (2010) [arXiv:1003.5018 [hep-th]].
[220] H., Elvang and M., Kiermaier, “Stringy KLT relations, global symmetries, and E7(7) violation,”JHEP 1010, 108 (2010) [arXiv:1007.4813 [hep-th]].
[221] N., Beisert, H., Elvang, D. Z., Freedman, et al., “E7(7) constraints on counterterms in N = 8 supergravity,”Phys. Lett. B 694, 265 (2010) [arXiv:1009.1643 [hep-th]].
[222] P., van Nieuwenhuizen and C. C., Wu, “On integral relations for invariants constructed from three riemann tensors and their applications in quantum gravity,”J. Math. Phys. 18, 182 (1977).
[223] G., Bossard, C., Hillmann, and H., Nicolai, “E7(7) symmetry in perturbatively quantised N = 8 supergravity,”JHEP 1012, 052 (2010) [arXiv:1007.5472 [hep-th]].
[224] D. Z., Freedman and E., Tonni, “The D2kR4 invariants of N = 8 supergravity,”JHEP 1104, 006 (2011) [arXiv:1101.1672 [hep-th]].
[225] S., Deser and J. H., Kay, “Three loop counterterms for extended supergravity,”Phys. Lett. B 76, 400 (1978).
[226] J. M., Drummond, P. J., Heslop, and P. S., Howe, “A note on N = 8 counterterms,” [arXiv:1008.4939 [hep-th]].
[227] G., Bossard and H., Nicolai, “Counterterms vs. dualities,”JHEP 1108, 074 (2011) [arXiv:1105.1273 [hep-th]].
[228] R., Kallosh and T., Kugo, “The footprint of E(7(7)) amplitudes of N = 8 supergravity,”JHEP 0901, 072 (2009) [arXiv:0811.3414 [hep-th]];
R., Kallosh, “E7(7) symmetry and finiteness of N = 8 supergravity,”JHEP 1203, 083 (2012) [arXiv:1103.4115 [hep-th]];
R., Kallosh, “N = 8 counterterms and E7(7) current conservation,”JHEP 1106, 073 (2011) [arXiv:1104.5480 [hep-th]];
R., Kallosh and T., Ortin, “New E77 invariants and amplitudes,”JHEP 1209, 137 (2012) [arXiv:1205.4437 [hep-th]];
M., Gunaydin and R., Kallosh, “Obstruction to E7(7) deformation in N = 8 supergravity,” [arXiv:1303.3540 [hep-th]];
J. J. M., Carrasco and R., Kallosh, “Hidden supersymmetry may imply duality invariance,” [arXiv:1303.5663 [hep-th]].
[229] S., Stieberger and T. R., Taylor, “Complete six-gluon disk amplitude in superstring theory,”Nucl. Phys. B 801, 128 (2008) [arXiv:0711.4354 [hep-th]].
[230] J., Broedel and L. J., Dixon, “R**4 counterterm and E(7)(7) symmetry in maximal supergravity,”JHEP 1005, 003 (2010) [arXiv:0911.5704 [hep-th]].
[231] N., Berkovits, “New higher-derivative R**4 theorems,”Phys. Rev. Lett. 98, 211601 (2007) [arXiv:hep-th/0609006];
M. B., Green, J. G., Russo, and P., Vanhove, “Non-renormalisation conditions in type II string theory and maximal supergravity,”JHEP 0702, 099 (2007) [arXiv:hep-th/0610299];
M. B., Green, J. G., Russo, and P., Vanhove, “Ultraviolet properties of maximal supergravity,”Phys. Rev. Lett. 98, 131602 (2007) [arXiv:hep-th/0611273];
M. B., Green, J. G., Russo, and P., Vanhove, “Modular properties of two-loop maximal supergravity and connections with string theory,”JHEP 0807, 126 (2008) [arXiv:0807.0389 [hep-th]];
N., Berkovits, M. B., Green, J. G., Russo, and P., Vanhove, “Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory,”JHEP 0911, 063 (2009) [arXiv:0908.1923 [hep-th]];
P., Vanhove, “The critical ultraviolet behaviour of N = 8 supergravity amplitudes,” [arXiv:1004.1392 [hep-th]].
[232] Z., Bern, J. J. M., Carrasco, L. J., Dixon, H., Johansson, and R., Roiban, “Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes,”Phys. Rev. D 85, 105014 (2012) [arXiv:1201.5366 [hep-th]].
[233] P. S., Howe and U., Lindstrom, “Higher order invariants in extended supergravity,”Nucl. Phys. B 181, 487 (1981).
[234] R. E., Kallosh, “Counterterms in extended supergravities,”Phys. Lett. B 99, 122 (1981).
[235] G., Bossard, P. S., Howe, K. S., Stelle, and P., Vanhove, “The vanishing volume of D = 4 superspace,”Class. Quant. Grav. 28, 215005 (2011) [arXiv:1105.6087 [hep-th]].
[236] N., Berkovits, “Super Poincare covariant quantization of the superstring,”JHEP 0004, 018 (2000) [hep-th/0001035].
[237] M. B., Green, H., Ooguri, and J. H., Schwarz, “Nondecoupling of maximal supergravity from the superstring,”Phys. Rev. Lett. 99, 041601 (2007) [arXiv:0704.0777 [hep-th]].
[238] T., Banks, “Arguments against a finite N = 8 supergravity,” [arXiv:1205.5768 [hep-th]].
[239] M., Bianchi, S., Ferrara, and R., Kallosh, “Perturbative and non-perturbative N = 8 supergravity,”Phys. Lett. B 690, 328 (2010) [arXiv:0910.3674 [hep-th]].
[240] Z., Bern, S., Davies, T., Dennen, Y.-t., Huang, and J., Nohle, “Color-kinematics duality for pure Yang–Mills and gravity at one and two loops,” [arXiv:1303.6605 [hep-th]].
[241] Z., Bern, S., Davies, T., Dennen, A. V., Smirnov, and V. A., Smirnov, “The ultraviolet properties of N = 4 supergravity at four loops,”Phys. Rev. Lett. 111, 231302 (2013) [arXiv:1309.2498 [hep-th]].
[242] Z., Bern, L. J., Dixon, D. C., Dunbar, M., Perelstein, and J. S., Rozowsky, “On the relationship between Yang–Mills theory and gravity and its implication for ultraviolet divergences,”Nucl. Phys. B 530, 401 (1998) [hep-th/9802162].
[243] D. C., Dunbar, B., Julia, D., Seminara, and M., Trigiante, “Counterterms in type I supergravities,”JHEP 0001, 046 (2000) [hep-th/9911158].
[244] Z., Bern, S., Davies, T., Dennen, and Y.-t., Huang, “Ultraviolet cancellations in half-maximal supergravity as a consequence of the double-copy structure,”Phys. Rev. D 86, 105014 (2012) [arXiv:1209.2472 [hep-th]].
[245] Z., Bern, S., Davies, T., Dennen, 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]];
[246] M., Fischler, “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).
[247] Z., Bern, S., Davies, and T., Dennen, “The ultraviolet structure of half-maximal supergravity with matter multiplets at two and three loops,” [arXiv:1305.4876 [hep-th]].
[248] G., Bossard, P. S., Howe, and K. S., Stelle, “Invariants and divergences in half-maximal supergravity theories,” [arXiv:1304.7753 [hep-th]].
[249] D., Vaman and Y.-P., Yao, “Constraints and generalized gauge transformations on tree-level gluon and graviton amplitudes,”JHEP 1011, 028 (2010) [arXiv:1007.3475 [hep-th]].
[250] R. H., Boels and R. S., Isermann, “On powercounting in perturbative quanturn gravity theories through color-kinematic duality,”JHEP 1306, 017 (2013) [arXiv:1212.3473].
[251] Z., Bern, T., Dennen, Y.-t., Huang, and M., Kiermaier, “Gravity as the square of gauge theory,”Phys.Rev. D 82, 065003 (2010) [arXiv:1004.0693 [hep-th]].
[252] M., Kiermaier, Talk at Amplitudes 2010, May 2010 at QMUL, London, UK. http://www.strings.ph.qmul.ac.uk/~theory/Amplitudes2010/
[253] N. E. J., Bjerrum-Bohr, P. H., Damgaard, T., Sondergaard, and P., Vanhove, “The momentum kernel of gauge and gravity theories,”JHEP 1101, 001 (2011) [arXiv:1010.3933 [hep-th]].
[254] C. R., Mafra, O., Schlotterer, and S., Stieberger, “Explicit BCJ numerators from pure spinors,”JHEP 1107, 092 (2011) [arXiv:1104.5224 [hep-th]];
C.-H., Fu, Y.-J., Du, and B., Feng, “An algebraic approach to BCJ numerators,”JHEP 1303, 050 (2013) [arXiv:1212.6168 [hep-th]].
[255] N. E. J., Bjerrum-Bohr, P. H., Damgaard, and P., Vanhove, “Minimal basis for gauge theory amplitudes,”Phys. Rev. Lett. 103, 161602 (2009) [0907.1425 [hep-th]];
S., Stieberger, “Open & closed vs. pure open string disk amplitudes,” [arXiv: 0907.2211 [hep-th]];
C. R., Mafra and O., Schlotterer, “The structure of n-point one-loop open superstring amplitudes,” [arXiv:1203.6215 [hep-th]];
O., Schlotterer and S., Stieberger, “Motivic multiple zeta values and superstring amplitudes,” [arXiv:1205.1516 [hep-th]];
J., Broedel, O., Schlotterer, and S., Stieberger, “Polylogarithms, multiple zeta values and superstring amplitudes,” [arXiv:1304.7267 [hep-th]].
[256] S. H., Henry Tye and Y., Zhang, “Dual identities inside the gluon and the graviton scattering amplitudes,”JHEP 1006, 071 (2010) [Erratum-ibid>. 1104, 114 (2011)] [arXiv:1003.1732 [hep-th]].
[257] B., Feng, R., Huang, and Y., Jia, “Gauge amplitude identities by on-shell recursion relation in s-matrix program,”Phys. Lett. B 695, 350 (2011) [arXiv:1004.3417 [hep-th]].
[258] F., Cachazo, “Fundamental BCJ relation in N = 4 SYM from the connected formulation,” [arXiv:1206.5970 [hep-th]].
[259] N. E. J., Bjerrum-Bohr, P. H., Damgaard, R., Monteiro, and D., O'Connell, “Algebras for amplitudes,”JHEP 1206, 061 (2012) [arXiv:1203.0944 [hep-th]].
[260] R., Monteiro and D., O'Connell, “The kinematic algebra from the self-dual sector,”JHEP 1107, 007 (2011) [arXiv:1105.2565 [hep-th]].
[261] M., Tolotti and S., Weinzierl, “Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality,” [arXiv:1306.2975 [hep-th]].
[262] Z., Bern, J. J. M., Carrasco, and H., Johansson, “Perturbative quantum gravity as a double copy of gauge theory,”Phys. Rev. Lett. 105, 061602 (2010) [arXiv:1004.0476 [hep-th]].
[263] J. J., Carrasco and H., Johansson, “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]].
[264] N. E. J., Bjerrum-Bohr, T., Dennen, R., Monteiro, and D., O'Connell, “Integrand oxidation and one-loop colour-dual numerators inN = 4 gauge theory,” [arXiv:1303.2913 [hep-th]].
[265] R. H., Boels, R. S., Isermann, R., Monteiro, and D., O'Connell, “Colour-kinematics duality for one-loop rational amplitudes,”JHEP 1304, 107 (2013) [arXiv:1301.4165 [hep-th]].
[266] J. J. M., Carrasco, M., Chiodaroli, M., Günaydin, and R., Roiban, “One-loop four-point amplitudes in pure and matter-coupled N ≤ 4 supergravity,”JHEP 1303, 056 (2013) [arXiv:1212.1146 [hep-th]].
[267] M., Chiodaroli, Q., Jin, and R., Roiban, “Color/kinematics duality for general abelian orbifolds of N = 4 super Yang-Mills theory,”JHEP 1401, 152 (2014) [arXiv:1311.3600 [hep-th]].
[268] J., Nohle, “Color-kinematics duality in one-loop four-gluon amplitudes with matter,” [arXiv:1309.7416 [hep-th]].
[269] Z., Bern, C., Boucher-Veronneau, and H., Johansson, “N ≥ 4 supergravity amplitudes from gauge theory at one loop,”Phys. Rev. D 84, 105035 (2011) [arXiv:1107.1935 [hep-th]];
C., Boucher-Veronneau and L. J., Dixon, “N ≥ 4 supergravity amplitudes from gauge theory at two loops,”JHEP 1112, 046 (2011) [arXiv:1110.1132 [hep-th]].
[270] M. T., Grisaru and W., Siegel, “Supergraphity. 2. Manifestly covariant rules and higher loop muteness,”Nucl. Phys. B 201, 292 (1982) [Erratum-ibid. B 206, 496 (1982)].
[271] S., Ferrara, R., Kallosh, and A., Van Proeyen, “Conjecture on hidden superconformal symmetry of N = 4 supergravity,”Phys. Rev. D 87, 025004 (2013) [arXiv:1209.0418 [hep-th]].
[272] J., Broedel and L. J., Dixon, “Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators,”JHEP 1210, 091 (2012) [arXiv:1208.0876 [hep-th]].
[273] R. H., Boels, B. A., Kniehl, O. V., Tarasov, and G., Yang, “Color-kinematic duality for form factors,”JHEP 1302, 063 (2013) [arXiv:1211.7028 [hep-th]];
[274] T., Bargheer, S., He, and T., McLoughlin, “New relations for three-dimensional supersymmetric scattering amplitudes,”Phys. Rev. Lett. 108, 231601 (2012) [arXiv:1203.0562 [hep-th]].
[275] Y.-t., Huang and H., Johansson, “Equivalent D = 3 supergravity amplitudes from double copies of three-algebra and two-algebra gauge theories,” [arXiv:1210.2255 [hep-th]].
[276] A., Zee, “Quantum field theory in a nutshell,”Princeton, USA: Princeton University Press (2010).
[277] M. D., Schwartz, Quantum Field Theory and the Standard Model, Cambridge, UK: Cambridge University Press (2013).
[278] J. M., Henn and J. C., Plefka, “Scattering amplitudes in gauge theories,”Lecture Notes in Physics 883Heidelbera: Springer (2014).
[279] M., Wolf, “A first course on twistors, integrability and gluon scattering amplitudes,”J. Phys. A 43, 393001 (2010) [arXiv:1001.3871 [hep-th]].
[280] Z., Bern, L. J., Dixon, and D. A., Kosower, “On-shell methods in perturbative QCD,”Annals Phys. 322, 1587 (2007) [arXiv:0704.2798 [hep-ph]].
[281] M. E., Peskin, “Simplifying multi-jet QCD computation,” [arXiv:1101.2414 [hep-ph]].
[282] J. F., Donoghue, “Introduction to the effective field theory description of gravity,” gr-qc/9512024.
[283] L. J., Dixon, “Ultraviolet behavior of N = 8 supergravity,” [arXiv:1005.2703 [hep-th]].
[284] Z., Bern, P., Gondolo, and M., Perelstein, “Neutralino annihilation into two photons,”Phys. Lett. B 411, 86 (1997) [hep-ph/9706538];
Z., Bern, A., De Freitas, and L. J., Dixon, “Two loop helicity amplitudes for gluon–gluon scattering in QCD and supersymmetric Yang–Mills theory,”JHEP 0203, 018 (2002) [hep-ph/0201161];
Z., Bern, A., De Freitas, and L. J., Dixon, “Two loop helicity amplitudes for quark gluon scattering in QCD and gluino gluon scattering in supersymmetric Yang–Mills theory,”JHEP 0306, 028 (2003) [hep-ph/0304168].
[285] S. J., Bidder, N. E. J., Bjerrum-Bohr, D. C., Dunbar, and W. B., Perkins, “One-loop gluon scattering amplitudes in theories with N < 4 supersymmetries,”Phys. Lett. B 612, 75 (2005) [hep-th/0502028].
[286] R., Britto, E., Buchbinder, F., Cachazo, and B., Feng, “One-loop amplitudes of gluons in SQCD,”Phys. Rev. D 72, 065012 (2005) [hep-ph/0503132].
[287] S., Lal and S., Raju, “Rational terms in theories with matter,”JHEP 1008, 022 (2010) [arXiv:1003.5264 [hep-th]].
[288] S., Dittmaier, “Weyl-van der Waerden formalism for helicity amplitudes of massive particles,”Phys. Rev. D 59, 016007 (1998) [hep-ph/9805445].
[289] R., Boels and C., Schwinn, “CSW rules for massive matter legs and glue loops,”Nucl. Phys. Proc. Suppl. 183, 137 (2008) [arXiv:0805.4577 [hep-th]].
[290] R. H., Boels, “No triangles on the moduli space of maximally supersymmetric gauge theory,”JHEP 1005, 046 (2010) [arXiv:1003.2989 [hep-th]].
[291] P., Ferrario, G., Rodrigo, and P., Talavera, “Compact multigluonic scattering amplitudes with heavy scalars and fermions,”Phys. Rev. Lett. 96, 182001 (2006) [hep-th/0602043].
[292] D., Forde and D. A., Kosower, “All-multiplicity amplitudes with massive scalars,”Phys. Rev. D 73, 065007 (2006) [hep-th/0507292].
[293] G., Rodrigo, “Multigluonic scattering amplitudes of heavy quarks,”JHEP 0509, 079 (2005) [hep-ph/0508138].
[294] C., Cheung, D., O'Connell, and B., Wecht, “BCFW recursion relations and string theory,”JHEP 1009, 052 (2010) [arXiv:1002.4674 [hep-th]].
[295] R. H., Boels, D., Marmiroli, and N. A., Obers, “On-shell recursion in string theory,”JHEP 1010, 034 (2010) [arXiv:1002.5029 [hep-th]].
[296] K., Kampf, J., Novotny, and J., Trnka, “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]].
[297] Z., Bern, L. J., Dixon, and D. A., Kosower, “The last of the finite loop amplitudes in QCD,”Phys.Rev. D 72, 125003 (2005) [hep-ph/0505055].
[298] B., Feng and M., Luo, “An introduction to on-shell recursion relations,” [arXiv:1111.5759 [hep-th]].
[299] J. M., Drummond, G. P., Korchemsky, and E., Sokatchev, “Conformal properties of four-gluon planar amplitudes and Wilson loops,”Nucl. Phys. B 795, 385 (2008) [arXiv:0707.0243 [hep-th]].
[300] N., Berkovits and J., Maldacena, “Fermionic T-duality, dual superconformal symmetry, and the amplitude/Wilson loop connection,”JHEP 0809, 062 (2008) [arXiv:0807.3196 [hep-th]].
[301] N., Beisert, R., Ricci, A. A., Tseytlin, and M., Wolf, “Dual superconformal symmetry from AdS(5) x S**5 superstring integrability,”Phys. Rev. D 78, 126004 (2008) [arXiv:0807.3228 [hep-th]].
[302] A., Brandhuber, P., Heslop, and G., Travaglini, “MHV amplitudes in N = 4 super Yang-Mills and Wilson loops,”Nucl. Phys. B 794, 231 (2008) [arXiv:0707.1153 [hep-th]].
[303] L. J., Mason and D., Skinner, “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]].
[304] S., Caron-Huot, “Notes on the scattering amplitude / Wilson loop duality,”JHEP 1107, 058 (2011) [arXiv:1010.1167 [hep-th]].
[305] B., Eden, P., Heslop, G. P., Korchemsky, and E., Sokatchev, “The super-correlator/superamplitude duality: Part I,”Nucl. Phys. B 869, 329 (2013) [arXiv:1103.3714 [hep-th]]; Part II, Nucl. Phys. B 869, 378 (2013) [arXiv:1103.4353 [hep-th]].
[306] L. F., Alday, B., Eden, G. P., Korchemsky, J., Maldacena, and E., Sokatchev, “From correlation functions to Wilson loops,”JHEP 1109, 123 (2011) [arXiv:1007.3243 [hep-th]].
[307] T., Adamo, M., Bullimore, L., Mason, and D., Skinner, “A proof of the supersym-metric correlation function / Wilson loop correspondence,”JHEP 1108, 076 (2011) [arXiv:1103.4119 [hep-th]].
[308] L. F., Alday and R., Roiban, “Scattering amplitudes, Wilson loops and the string/gauge theory correspondence,”Phys. Rept. 468, 153 (2008) [arXiv:0807.1889 [hep-th]].
[309] R. M., Schabinger, “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]].
[310] J. M., Henn, “Duality between Wilson loops and gluon amplitudes,”Fortsch. Phys. 57, 729 (2009) [arXiv:0903.0522 [hep-th]].
[311] T., Adamo, M., Bullimore, L., Mason, and D., Skinner, “Scattering amplitudes and Wilson loops in twistor space,”J. Phys. A 44, 454008 (2011) [arXiv:1104.2890 [hep-th]].
[312] L. F., Alday, D., Gaiotto, J., Maldacena, A., Sever, and P., Vieira, “An operator product expansion for polygonal null Wilson loops,”JHEP 1104, 088 (2011) [arXiv:1006.2788 [hep-th]].
[313] B., Basso, A., Sever, and P., Vieira, “Space-time S-matrix and flux-tube S-matrix at finite coupling,”Phys. Rev. Lett. 111, 091602 (2013) [arXiv:1303.1396 [hep-th]].
[314] B., Basso, A., Sever, and P., Vieira, “Space-time S-matrix and flux tube S-matrix II. Extracting and matching data,”JHEP 1401, 008 (2014) [arXiv:1306.2058 [hep-th]].
[315] B., Basso, A., Sever, and P., Vieira, “Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions,” [arXiv:1402.3307 [hep-th]].
[316] L. J., Dixon, J. M., Drummond, M., von Hippel, and J., Pennington, “Hexagon functions and the three-loop remainder function,”JHEP 1312, 049 (2013) [arXiv:1308.2276 [hep-th]].
[317] L. J., Dixon, J. M., Drummond, C., Duhr, and J., Pennington, “The four-loop remainder function and multi-Regge behavior at NNLLA in planar N = 4 super-Yang-Mills theory,” [arXiv:1402.3300 [hep-th]].
[318] R., Penrose and W., Rindler, Spinors and Space-Time, vol. 2, Cambridge: Cambridge University Press (1986).
[319] R., Ward and R., Wells, Twistor Geometry and Field Theory, Cambridge: Cambridge University Press (1990).
[320] S., Huggett and P., Tod, An Introduction to Twistor Theory, Student Texts 4, London: London Mathematical Society (1985).
[321] F., Cachazo and P., Svrcek, “Lectures on twistor strings and perturbative Yang–Mills theory,”PoS RTN 2005, 004 (2005) [hep-th/0504194].