An introduction to on-shell recursion relations

Abstract

This article provides an introduction to on-shell recursionrelations for calculations of tree-level amplitudes. Starting withthe basics, such as spinor notations and color decompositions, weexpose analytic properties of gauge-boson amplitudes, BCFW-deformations,the large z-behavior of amplitudes, and on-shell recursion relationsof gluons. We discuss further developments of on-shell recursion relations,including generalization to other quantum field theories, supersymmetrictheories 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 relationsin 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 consistentconditions under recursion relation, Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson(BCJ) relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye(KLT) relations.

Keywords

amplitude / on-shell recursionrelation

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