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### Book description

Providing a comprehensive, pedagogical introduction to scattering amplitudes in gauge theory and gravity, this book is ideal for graduate students and researchers. It offers a smooth transition from basic knowledge of quantum field theory to the frontier of modern research. Building on basic quantum field theory, the book starts with an introduction to the spinor helicity formalism in the context of Feynman rules for tree-level amplitudes. The material covered includes on-shell recursion relations, superamplitudes, symmetries of N=4 super Yang–Mills theory, twistors and momentum twistors, Grassmannians, and polytopes. The presentation also covers amplitudes in perturbative supergravity, 3D Chern–Simons matter theories, and color-kinematics duality and its connection to 'gravity=(gauge theory)x(gauge theory)'. Basic knowledge of Feynman rules in scalar field theory and quantum electrodynamics is assumed, but all other tools are introduced as needed. Worked examples demonstrate the techniques discussed, and over 150 exercises help readers absorb and master the material.

### Reviews

‘In recent years, a series of surprising insights and new methods have transformed the understanding of gauge and gravitational scattering amplitudes. These advances are important both for practical calculations in particle physics, and for the fundamental structure of relativistic quantum theory. Elvang and Huang have written the first comprehensive text on this subject, and their clear and pedagogical approach will make these new ideas accessible to a wide range of students.’

Joseph Polchinski - University of California, Santa Barbara

‘This book provides a much-needed text covering modern techniques that have given radical new insights into the structure of quantum field theory. It gathers together a very large body of recent literature and presents it in a coherent style. The book should appeal to the wide body of researchers who wish to use quantum field theory as a tool for describing physical phenomena or who are intending to gain insight by studying its mathematical structure.’

Michael B. Green - University of Cambridge

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## Contents

• ##### Index pp 319-323
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[110] , , and , “An analytic result for the two-loop hexagon Wilson loop in N = 4SYM,”JHEP 1003, 099 (2010) [arXiv:0911.5332 [hep-ph]].
[111] , , and , “The two-loop hexagon Wilson loop in N = 4 SYM,”JHEP 1005, 084 (2010) [arXiv:1003.1702 [hep-th]].
[112] , , , and , “Classical polylogarithms for amplitudes and Wilson loops,”Phys. Rev. Lett. 105, 151605 (2010) [arXiv:1006.5703 [hep-th]].
[113] and , “One-loop gluonic amplitudes from single unitarity cuts,”JHEP 0812, 067 (2008) [0810.2964 [hep-th]];
, , , and , “A tree-loop duality relation at two loops and beyond,”JHEP 1010, 073 (2010) [arXiv:1007.0194 [hep-ph]];
, , and , “Integrands for QCD rational terms and N = 4 SYM frommassive CSW rules,”JHEP 1206, 015 (2012) [arXiv:1111.0635 [hep-th]].
[114] , “Loops and trees,”JHEP 1105, 080 (2011) [arXiv:1007.3224 [hep-ph]].
[115] , , , , and , “The all-loop integrand for scattering amplitudes in planar N = 4 SYM,”JHEP 1101, 041 (2011) [arXiv:1008.2958 [hep-th]].
[116] , “On BCFW shifts of integrands and integrals,”JHEP 1011, 113 (2010) [arXiv:1008.3101 [hep-th]].
[117] , , , and , “Maximally supersymmetric planar Yang–Mills amplitudes at five loops,”Phys.Rev. D 76, 125020 (2007) [0705.1864 [hep-th]].
[118] , , and , “Generalized unitarity and one-loop amplitudes in N = 4 super-Yang–Mills,”Nucl. Phys. B 725, 275 (2005) [hep-th/0412103];
and , “Two-loop amplitudes of gluons and octa-cuts in N = 4 super Yang–Mills,”JHEP 0511, 036 (2005) [hep-th/0506126].
[119] , , , and , “Local integrals for planar scattering amplitudes,”JHEP 1206, 125 (2012) [arXiv:1012.6032 [hep-th]].
For extensions, see , , and , “Dual-conformal regularization of infrared loop divergences and the chiral box expansion,” [arXiv:1303.4734 [hep-th]].
[120] , , , et al., “Scattering amplitudes and the positive Grassmannian,” [arXiv:1212.5605 [hep-th]].
[121] , “Sharpening the leading singularity,” [arXiv:0803.1988 [hep-th]].
[122] and , “Yangians, Grassmannians and T-duality,”JHEP 1007, 027 (2010) [arXiv:1001.3348 [hep-th]].
[123] and , “The Yangian origin of the Grassmannian integral,”JHEP 1012, 010 (2010) [arXiv:1002.4622 [hep-th]];
and , “Superconformal invariants for scattering amplitudes in N = 4 SYM theory,”Nucl. Phys. B 839, 377 (2010) [arXiv:1002.4625 [hep-th]].
[124] , , and , “On the tree level S matrix of Yang–Mills theory,”Phys. Rev. D 70, 026009 (2004) [hep-th/0403190].
[125] and , “From twistor string theory to recursion relations,”Phys. Rev. D 80, 085022 (2009) [arXiv:0909.0229 [hep-th]].
[126] , , , and , “Unification of residues and Grassmannian dualities,”JHEP 1101, 049 (2011) [arXiv:0912.4912 [hep-th]].
[127] , , , and , “The Grassmannian and the twistor string: Connecting all trees in N = 4 SYM,”JHEP 1101, 038 (2011) [arXiv:1006.1899 [hep-th]].
[128] , , and , “Twistor-strings, Grassmannians and leading singularities,”JHEP 1003, 070 (2010) [arXiv:0912.0539 [hep-th]].
[129] and , “Complete equivalence between gluon tree amplitudes in twistor string theory and in gauge theory,”JHEP 1206, 030 (2012) [arXiv:1111.0950 [hep-th]].
[130] , , , , and , “A note on polytopes for scattering amplitudes,”JHEP 1204, 081 (2012) [arXiv:1012.6030 [hep-th]].
[131] , , and , “MHV diagrams in momentum twistor space,”JHEP 1012, 032 (2010) [arXiv:1009.1854 [hep-th]].
[132] and , “The amplituhedron,” [arXiv:1312.2007 [hep-th]];
and , “Into the amplituhedron,” [arXiv:1312.7878 [hep-th]].
[133] and , “Amplitudes at weak coupling as polytopes in AdS5,”J. Phys. A 44, 135401 (2011) [arXiv:1004.3498 [hep-th]].
[134] and , “Twistor and polytope interpretations for subleading color one-loop amplitudes,”Nucl. Phys. B 855, 901 (2012) [arXiv:1104.2752 [hep-th]].
[135] , “Covariant representation theory of the Poincaré algebra and some of its extensions,”JHEP 1001, 010 (2010) [arXiv:0908.0738 [hep-th]].
[136] and , “Spinor helicity and dual conformal symmetry in ten dimensions,”JHEP 1108, 014 (2011) [arXiv:1010.5487 [hep-th]].
[137] and , “Simple superamplitudes in higher dimensions,”JHEP 1206, 163 (2012) [arXiv:1201.2653 [hep-th]].
[138] , “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] , , , , and , “Generalized unitarity and six-dimensional helicity,”Phys. Rev. D 83, 085022 (2011) [arXiv:1010.0494 [hep-th]].
[140] , , , and , “Massive amplitudes on the Coulomb branch of N = 4SYM,”JHEP 1112, 097 (2011) [arXiv:1104.2050 [hep-th]].
[141] and , “Amplitudes and spinor-helicity in six dimensions,”JHEP 0907, 075 (2009) [arXiv:0902.0981 [hep-th]].
[142] , , and , “Supertwistor space for 6D maximal super Yang–Mills,”JHEP 1004, 127 (2010) [arXiv:0910.2688 [hep-th]].
[143] , , , and , “One-loop amplitudes in six-dimensional (1,1) theories from generalised unitarity,”JHEP 1102, 077 (2011) [arXiv:1010.1515 [hep-th]];
, , and , “A twistor description of six-dimensional N = (1,1) super Yang–Mills theory,”JHEP 1205, 020 (2012) [arXiv:1201.6285 [hep-th]].
[144] and , “Dual conformal properties of six-dimensional maximal super Yang–Mills amplitudes,”JHEP 1101, 140 (2011) [arXiv:1010.5874 [hep-th]].
[145] , “Superconformal field theory in six dimensions and supertwistor,” [arXiv:0906.0657 [hep-th]];
, , and , “Superconformalsymmetry, and maximal supergravity in various dimensions,”JHEP 1203, 093 (2012) [arXiv:1108.3085 [hep-th]];
, , and , “Conformal field theories in six-dimensional twistor space,”J. Geom. Phys. 62, 2353 (2012) [arXiv:1111.2585 [hep-th]];
and , “On twistors and conformal field theories from six dimensions,”J. Math. Phys. 54, 013507 (2013) [arXiv:1111.2539 [hep-th]].
[146] , , and , “Amplitudes for multiple M5 branes,”JHEP 1210, 143 (2012) [arXiv:1110.2791 [hep-th]].
[147] and , “Non-Abelian tensor multiplet equations from twistor space,” [arXiv:1205.3108 [hep-th]].
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