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arxiv: 1203.0944 · v2 · pith:JNBKKGXQnew · submitted 2012-03-05 · ✦ hep-th

Algebras for Amplitudes

classification ✦ hep-th
keywords amplitudesbasisgaugecolor-kinematicsdualityrelationstheoryvertices
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Tree-level amplitudes of gauge theories are expressed in a basis of auxiliary amplitudes with only cubic vertices. The vertices in this formalism are explicitly factorized in color and kinematics, clarifying the color-kinematics duality in gauge theory amplitudes. The basis is constructed making use of the KK and BCJ relations, thereby showing precisely how these relations underlie the color-kinematics duality. We express gravity amplitudes in terms of a related basis of color-dressed gauge theory amplitudes, with basis coefficients which are permutation symmetric.

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Cited by 2 Pith papers

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  1. $D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions

    hep-ph 2025-11 unverdicted novelty 7.0

    A modular assembly method constructs D-dimensional higher-derivative four-point amplitudes involving fermions from gauge-invariant blocks, color factors, and permutation-invariant scalar polynomials.

  2. Amplitudes in self-dual (higher-spin) theories

    hep-th 2026-04 unverdicted novelty 6.0

    All self-dual theories with or without higher-spin fields possess nontrivial tree-level amplitudes in Kleinian or complex Minkowski kinematics, completing the celestial analogue of the higher-spin duality.