Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry
arXiv:2103.13908 · doi:10.1007/JHEP07(2021)111
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.
arXiv comment44 pages, 19 figures
References in corpus (15)
- New Relations for Gauge-Theory Amplitudes
- The Amplituhedron
- Scattering of Massless Particles: Scalars, Gluons and Gravitons
- New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
- Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
- Positive Geometries and Canonical Forms
- Scattering amplitudes: the most perfect microscopic structures in the universe
- The Momentum Amplituhedron
- Notes on Scattering Amplitudes as Differential Forms
- Cluster Adjacency for m=2 Yangian Invariants
- Positive geometry, local triangulations, and the dual of the Amplituhedron
- From Momentum Amplituhedron Boundaries to Amplitude Singularities and Back
- Amplituhedra, and Beyond
- Boundaries of the Amplituhedron with amplituhedronBoundaries
- 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