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The purpose of this review is to bridge the gap between a standard course in quantum field theory and recent fascinating developments in the studies of on-shell scattering amplitudes.
A. Hodges, “A simple formula for gravitational MHV amplitudes,” arXiv:1204.1930 [hep-th]
1930
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P. A. M. Dirac, “Wave equations in conformal space,” Annals Math. 37
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R. Penrose, “Twistor algebra,” J. Math. Phys. 8
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S. Weinberg, “Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity,” USA, John Wiley & Sons (1972)
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B. S. DeWitt, “Quantum Theory of Gravity. 2. The Manifestly Covariant Theory,” Phys. Rev. 162
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1977
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B. de Wit and D. Z. Freedman, “On SO(8) Extended Supergravity,” Nucl. Phys. B 130
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M. T. Grisaru, “Two Loop Renormalizability of Supergravity,” Phys. Lett. B 66
1977
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E. Tomboulis, “On the Two Loop Divergences of Supersymmetric Gravitation,” Phys. Lett. B 67
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S. Deser, J. H. Kay and K. S. Stelle, “Renormalizability Properties of Supergravity,” Phys. Rev. Lett. 38
1977
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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
1977
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A. Ferber, “Supertwistors And Conformal Supersymmetry,” Nucl. Phys. B 132
1978
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S. Deser and J. H. Kay, “Three Loop Counterterms For Extended Supergravity,” Phys. Lett. B 76
1978
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L. M. Brown and R. P. Feynman, “Radiative corrections to Compton scattering,” Phys. Rev. 85
1979
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E. Cremmer and B. Julia, “The N=8 Supergravity Theory. 1. The Lagrangian,” Phys. Lett. B 80
1979
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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
1979
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P. S. Howe and U. Lindstrom, “Higher Order Invariants In Extended Supergravity,” Nucl. Phys. B 181
1981
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R. E. Kallosh, “Counterterms in extended supergravities,” Phys. Lett. B 99
1981
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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
1982
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B. de Wit and H. Nicolai, “N=8 Supergravity,” Nucl. Phys. B 208
1982
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M. T. Grisaru and W. Siegel, “Supergraphity. 2. Manifestly Covariant Rules and Higher Loop Finiteness,” Nucl. Phys. B 201
1982
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S. J. Gates, M. T. Grisaru, M. Rocek and W. Siegel, “Superspace Or One Thousand and One Lessons in Supersymmetry,” Front. Phys. 58
1983
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W. L. van Neerven and J. A. M. Vermaseren, “Large Loop Integrals,” Phys. Lett. B 137
1984
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R. M. Wald, “General Relativity,” Chicago, Usa: Univ. Pr. ( 1984) 491p
1984
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N. Marcus, “Composite Anomalies In Supergravity,” Phys. Lett. B 157
1985
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P. di Vecchia, S. Ferrara and L. Girardello, “Anomalies Of Hidden Local Chiral Symmetries In Sigma Models And Extended Supergravities,” Phys. Lett. B 151
1985
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M. H. Goroff and A. Sagnotti, “Quantum Gravity At Two Loops,” Phys. Lett. B 160
1985
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Student Texts 4. London Mathematical Society, 1985
S. Huggett and P. Tod, An Introduction to Twistor Theory · 1985
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H. Kawai, D. C. Lewellen and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl. Phys. B 269
1986
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S. Sannan, “Gravity As The Limit Of The Type II Superstring Theory,” Phys. Rev. D 34
1986
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Cambridge University Press, 1986
R. Penrose and W. Rindler, Spinors and Space-Time · 1986
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F. Cachazo, “Sharpening The Leading Singularity,” arXiv:0803.1988 [hep-th]
1988
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F. A. Berends, W. T. Giele and H. Kuijf, “On relations between multi-gluon and multigraviton scattering,” Phys. Lett. B 211
1988
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R. Kleiss and H. Kuijf, “Multi-Gluon Cross-sections And Five Jet Production At Hadron Colliders,” Nucl. Phys. B 312
1989
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C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, “D-dimensional unitarity cut method,” Phys. Lett. B 645
1989
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F. A. Berends and W. T. Giele, “Recursive Calculations for Processes with n Gluons,” Nucl. Phys. B 306
1990
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CUP, 1990
R. Ward and R. Wells, Twistor Geometry and Field Theory · 1990
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M. L. Mangano and S. J. Parke, “Multiparton amplitudes in gauge theories,” Phys. Rept. 200
1991
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J. Wess and J. Bagger, “Supersymmetry and supergravity,” Princeton, USA: Univ. Pr. (1992) 259 p
1992
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A. E. M. van de Ven, “Two loop quantum gravity,” Nucl. Phys. B 378
1992
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Z. Bern, L. J. Dixon and D. A. Kosower, “Dimensionally regulated one loop integrals,” Phys. Lett. B 302
1993
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W. Siegel, “Two vierbein formalism for string inspired axionic gravity,” Phys. Rev. D 47
1993
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D. Z. Freedman, “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.) 19 p [hep-th/9408175]
1993
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Z. Bern, L. J. Dixon and D. A. Kosower, “Dimensionally regulated pentagon integrals,” Nucl. Phys. B 412
1994
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L. J. Dixon, “Calculating scattering amplitudes efficiently,” In *Boulder 1995, QCD and beyond* 539-582 [hep-ph/9601359]
1995
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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
1995
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Z. Bern and A. G. Morgan, “Massive Loop Amplitudes from Unitarity,” Nucl. Phys. B 467
1996
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Z. Bern, J. S. Rozowsky and B. Yan, “Two loop four gluon amplitudes in N=4 superYang-Mills,” Phys. Lett. B 401
1997
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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
1998
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S. Dittmaier, “Weyl-van der Waerden formalism for helicity amplitudes of massive particles,” Phys. Rev. D 59
1998
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Z. Bern, L. J. Dixon, M. Perelstein and J. S. Rozowsky, “Multileg one loop gravity amplitudes from gauge theory,” Nucl. Phys. B 546
1999
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Z. Bern and A. K. Grant, “Perturbative gravity from QCD amplitudes,” Phys. Lett. B 457
1999
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V. Del Duca, L. J. Dixon and F. Maltoni, “New color decompositions for gauge amplitudes at tree and loop level,” Nucl. Phys. B 571
2000
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Z. Bern, L. J. Dixon, D. C. Dunbar, A. K. Grant, M. Perelstein and J. S. Rozowsky, “On perturbative gravity and gauge theory,” Nucl. Phys. Proc. Suppl. 88
2000
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N. Berkovits, “Super Poincare covariant quantization of the superstring,” JHEP 0004
2000
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D. C. Dunbar, B. Julia, D. Seminara and M. Trigiante, “Counterterms in type I supergravities,” JHEP 0001
2000
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Z. Bern, “Perturbative quantum gravity and its relation to gauge theory,” Living Rev. Rel. 5
2002
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C. Anastasiou, Z. Bern, L. J. Dixon and D. A. Kosower, “Planar amplitudes in maximally supersymmetric Yang-Mills theory,” Phys. Rev. Lett. 91
2003
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P. S. Howe and K. S. Stelle, “Supersymmetry counterterms revisited,” Phys. Lett. B 554
2003
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Z. Bern, P. Gondolo and M. Perelstein, “Neutralino annihilation into two photons,” Phys. Lett. B 411
2003
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F. Cachazo, P. Svrcek and E. Witten, “MHV vertices and tree amplitudes in gauge theory,” JHEP 0409
2004
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L. J. Dixon, E. W. N. Glover and V. V. Khoze, “MHV rules for Higgs plus multi-gluon amplitudes,” JHEP 0412
2004
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E. Witten, “Perturbative gauge theory as a string theory in twistor space,” Commun. Math. Phys. 252
2004
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R. Roiban, M. Spradlin and A. Volovich, “On the tree level S matrix of Yang-Mills theory,” Phys. Rev. D 70
2004
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S. M. Carroll, “Spacetime and geometry: An introduction to general relativity,” San Francisco, USA: Addison-Wesley (2004) 513p
2004
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R. Britto, F. Cachazo and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl. Phys. B 715
2005
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R. Britto, F. Cachazo, B. Feng and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys. Rev. Lett. 94
2005
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K. Risager, “A Direct proof of the CSW rules,” JHEP 0512
2005
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S. D. Badger, E. W. N. Glover and V. V. Khoze, “MHV rules for Higgs plus multi-parton amplitudes,” JHEP 0503
2005
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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
2005
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R. Britto, F. Cachazo and B. Feng, “Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills,” Nucl. Phys. B 725
2005
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J. Bedford, A. Brandhuber, B. J. Spence and G. Travaglini, “A Recursion relation for gravity amplitudes,” Nucl. Phys. B 721
2005
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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
2005
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R. Britto, E. Buchbinder, F. Cachazo and B. Feng, “One-loop amplitudes of gluons in SQCD,” Phys. Rev. D 72
2005
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G. Rodrigo, “Multigluonic scattering amplitudes of heavy quarks,” JHEP 0509
2005
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Z. Bern, L. J. Dixon and D. A. Kosower, “The last of the finite loop amplitudes in QCD,” Phys. Rev. D 72
2005
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F. Cachazo and P. Svrcek, “Lectures on twistor strings and perturbative Yang-Mills theory,” PoS RTN 2005
2005
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N. E. J. Bjerrum-Bohr, D. C. Dunbar, H. Ita, W. B. Perkins and K. Risager, “MHV-vertices for gravity amplitudes,” JHEP 0601
2006
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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
2006
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F. Cachazo, M. Spradlin and A. Volovich, “Iterative structure within the five-particle two-loop amplitude,” Phys. Rev. D 74
2006
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P. Ferrario, G. Rodrigo and P. Talavera, “Compact multigluonic scattering amplitudes with heavy scalars and fermions,” Phys. Rev. Lett. 96
2006
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D. Forde and D. A. Kosower, “All-multiplicity amplitudes with massive scalars,” Phys. Rev. D 73
2006
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M. Srednicki, “Quantum field theory,” Cambridge, UK: Univ. Pr. (2007) 641 p
2007
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P. Benincasa, C. Boucher-Veronneau and F. Cachazo, “Taming Tree Amplitudes In General Relativity,” JHEP 0711
2007
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Z. Bern, L. J. Dixon and D. A. Kosower, “On-Shell Methods in Perturbative QCD,” Annals Phys. 322
2007
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R. Boels, L. J. Mason and D. Skinner, “From twistor actions to MHV diagrams,” Phys. Lett. B 648
2007
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J. M. Drummond, J. Henn, V. A. Smirnov and E. Sokatchev, “Magic identities for conformal four-point integrals,” JHEP 0701
2007
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L. F. Alday and J. Maldacena, “Comments on gluon scattering amplitudes via AdS/CFT,” JHEP 0711
2007
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L. F. Alday and J. M. Maldacena, “Gluon scattering amplitudes at strong coupling,” JHEP 0706
2007
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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
2007
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2007
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H. Elvang and D. Z. Freedman, unpublished notes (2007)
2007
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Z. Bern, L. J. Dixon and R. Roiban, “Is N = 8 supergravity ultraviolet finite?,” Phys. Lett. B 644
2007
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R. H. Boels, “No triangles on the moduli space of maximally supersymmetric gauge theory,” JHEP 1005
2010
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C. Cheung, D. O’Connell and B. Wecht, “BCFW Recursion Relations and String Theory,” JHEP 1009
2010
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R. H. Boels, D. Marmiroli and N. A. Obers, “On-shell Recursion in String Theory,” JHEP 1010
2010
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2010
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Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson, D. A. Kosower and R. Roiban, “Three-Loop Superfiniteness of N=8 Supergravity,” Phys. Rev. Lett. 98
2007
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2007
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2008
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N. Arkani-Hamed and J. Kaplan, “On Tree Amplitudes in Gauge Theory and Gravity,” JHEP 0804
2008
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2008
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N. Arkani-Hamed, ”What is the Simplest QFT?,” talk given at the Paris Workshop Wonders of Gauge Theory and Supergravity , June 24, 2008
2008
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2008
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2010
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2011
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2011
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A. Brandhuber, B. Spence and G. Travaglini, “Tree-Level Formalism,” J. Phys. A 44
2011
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2011
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2011
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Z. Bern and Y.-t. Huang, “Basics of Generalized Unitarity,” J. Phys. A 44
2011
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H. Ita, “Susy Theories and QCD: Numerical Approaches,” J. Phys. A 44
2011
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R. Britto, “Loop Amplitudes in Gauge Theories: Modern Analytic Approaches,” J. Phys. A 44
2011
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2011
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H. Elvang, Y.-t. Huang and C. Peng, “On-shell superamplitudes in N < 4 N<4 SYM,” JHEP 1109
2011
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2011
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A. V. Smirnov and A. V. Petukhov, “The Number of Master Integrals is Finite,” Lett. Math. Phys. 97
2011
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S. Caron-Huot, “Loops and trees,” JHEP 1105
2011
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2011
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2011
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2011
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L. Mason and D. Skinner, “Amplitudes at Weak Coupling as Polytopes in AdS 5 ,” J. Phys. A 44
2011
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G. Bossard and H. Nicolai, “Counterterms vs. Dualities,” JHEP 1108
2011
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2011
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2011
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R. Monteiro and D. O’Connell, “The Kinematic Algebra From the Self-Dual Sector,” JHEP 1107
2011
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2011
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S. Caron-Huot, “Notes on the scattering amplitude / Wilson loop duality,” JHEP 1107
2011
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R. H. Boels and D. O’Connell, “Simple superamplitudes in higher dimensions,” JHEP 1206
2012
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2012
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B. Czech, Y.-t. Huang and M. Rozali, “Amplitudes for Multiple M5 Branes,” JHEP 1210
2012
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2012
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D. Z. Freedman and A. Van Proeyen, “Supergravity,” Cambridge, UK: Cambridge Univ. Pr. (2012) 607 p
2012
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R. Kallosh and T. Kugo, “The Footprint of E(7(7)) amplitudes of N=8 supergravity,” JHEP 0901
2012
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2012
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K. Kampf, J. Novotny and J. Trnka, “Tree-level Amplitudes in the Nonlinear Sigma Model,” JHEP 1305
2013
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A. Hodges, “Eliminating spurious poles from gauge-theoretic amplitudes,” JHEP 1305
2013
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2013
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D. A. Kosower and K. J. Larsen, “Maximal Unitarity at Two Loops,” Phys. Rev. D 85
2013
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M. S¿gaard, “Global Residues and Two-Loop Hepta-Cuts,” JHEP 1309
2013
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2013
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S. Caron-Huot and Y.-t. Huang, “The two-loop six-point amplitude in ABJM theory,” JHEP 1303
2013
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2014
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J. M. Henn and J. C. Plefka, “Scattering Amplitudes in Gauge Theories,” Lecture Notes in Physics 883 (2014), Springer
2014
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S. Badger, H. Frellesvig and Y. Zhang, “Hepta-Cuts of Two-Loop Scattering Amplitudes,” JHEP 1204
2019
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2050
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