Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry

Abstract

In recent years, it has been understood that color-ordered scattering amplitudes can be encoded as logarithmic differential forms on positive geometries. In particular, amplitudes in maximally supersymmetric Yang-Mills theory in spinor helicity space are governed by the momentum amplituhedron. Due to the group-theoretic structure underlying color decompositions, color-ordered amplitudes enjoy various identities which relate different orderings. In this paper, we show how the Kleiss-Kuijf relations arise from the geometry of the momentum amplituhedron. We also show how similar relations can be realised for the kinematic associahedron, which is the positive geometry of bi-adjoint scalar cubic theory.

44 pages, 19 figures

References in corpus (2)

• New Relations for Gauge-Theory Amplitudes
• Momentum Amplituhedron meets Kinematic Associahedron

Cited by in corpus (6)

• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• The orthogonal momentum amplituhedron and ABJM amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• Amplituhedron-like geometries
• Internal boundaries of the loop amplituhedron
• Positive Geometry for Stringy Scalar Amplitudes