Amplituhedron meets Jeffrey-Kirwan Residue

Understand

The tree amplituhedra $\mathcal{A}_{n,k}^{(m)}$ are mathematical objects generalising the notion of polytopes into the Grassmannian.

• Proposed for $m=4$ as a geometric construction encoding tree-level scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory, they are mathematically interesting for any $m$.
• In this paper we strengthen the relation between scattering amplitudes and geometry by linking the amplituhedron to the Jeffrey-Kirwan residue, a powerful concept in symplectic and algebraic geometry.
• We focus on a particular class of amplituhedra in any dimension, namely cyclic polytopes, and their even-dimensional conjugates.