Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry
David Damgaard, Livia Ferro, Tomasz Lukowski, Robert Moerman
TL;DR
This paper demonstrates how Kleiss-Kuijf relations in scattering amplitudes are derived from the geometric structure of the momentum amplituhedron and extends similar relations to the kinematic associahedron in scalar theories.
Contribution
It reveals the geometric origin of Kleiss-Kuijf relations from the momentum amplituhedron and connects these to the kinematic associahedron in scalar theories.
Findings
Kleiss-Kuijf relations are derived from the momentum amplituhedron geometry.
Similar relations are established for the kinematic associahedron.
The geometric perspective unifies amplitude identities across theories.
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.
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