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An Introduction to On-shell Recursion Relations

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arxiv 1111.5759 v3 pith:Z7FH4MXB submitted 2011-11-24 hep-th hep-ph

Bo Feng , Mingxing Luo This is my paper · ORCID
classification hep-thhep-ph
keywords relationsrecursionamplitudeson-shelltheoriesincludingintroductionrelation
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $N$-Photon Amplitudes in EFT from Recursion Relations and Effective Vertices

    hep-th 2026-08 conditional novelty 7.0 of 10

    A CSW-like recursion plus a 'contact Lagrangian' computes arbitrary tree-level N-photon amplitudes in general EFTs, with results through 10 photons in Born-Infeld theory.

  2. Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order $\boldsymbol{g}^{\boldsymbol{6}}$

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    An on-shell construction using BCFW trees plus vacuum-pair phase-space integrals with inclusion-exclusion signs reproduces the known one- and two-loop all-plus four-gluon amplitudes.

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