Landau Analysis in the Grassmannian

TL;DR

This paper develops a geometric Landau analysis for Feynman integrals using Grassmannian structures, linking algebraic geometry with particle physics amplitude computations and revealing positivity and cluster structures.

Contribution

It introduces a novel geometric framework connecting Landau analysis, Grassmannians, and the amplituhedron, advancing understanding of scattering amplitudes in supersymmetric theories.

Findings

Discriminants and resultants identified with Hurwitz and Chow forms.

Analysis of degrees and factorizations of these forms.

Insights into kinematic regimes with rational or real fibers.

Abstract

Momentum twistors for scattering amplitudes in particle physics are lines in three-space. We develop Landau analysis for Feynman integrals in this setting. The resulting discriminants and resultants are identified with Hurwitz and Chow forms of incidence varieties in products of Grassmannians. We study their degrees and factorizations, and the kinematic regimes in which the fibers of the Landau map are rational or real. Identifying this map with the amplituhedron map on positroid varieties, and the associated recursions with promotion maps, yields a geometric mechanism for the emergence of positivity and cluster structures in planar N=4 super Yang-Mills theory.