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An introduction to on-shell recursion relations

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Abstract

This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we expose analytic properties of gauge-boson amplitudes, BCFW-deformations, the large z-behavior of amplitudes, and on-shell recursion relations of gluons. We discuss further developments of on-shell recursion relations, including generalization to other quantum field theories, supersymmetric theories in particular, recursion relations for off-shell currents, recursion relation with nonzero boundary contributions, bonus relations, relations for rational parts of one-loop amplitudes, recursion relations in 3D and a proof of CSW rules. Finally, we present samples of applications, including solutions of split helicity amplitudes and of N = 4 SYM theories, consequences of consistent conditions under recursion relation, Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye (KLT) relations.

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Authors and Affiliations

  1. Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, 310027, China

    Bo Feng & Mingxing Luo

  2. Center of Mathematical Science, Zhejiang University, Hangzhou, 310027, China

    Bo Feng

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  1. Bo Feng
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  2. Mingxing Luo
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Correspondence to Mingxing Luo.

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Feng, B., Luo, M. An introduction to on-shell recursion relations. Front. Phys. 7, 533–575 (2012). https://doi.org/10.1007/s11467-012-0270-z

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