Spinor-Helicity Varieties

Abstract: The spinor-helicity formalism in particle physics gives rise to natural subvarieties in the product of two Grassmannians. These include two-step flag varieties for subspaces of complementary dimension. Taking Hadamard products leads to Mandelstam varieties. We study these varieties through the lens of combinatorics and commutative algebra, and we explore their tropicalization, positive geometry, and scattering correspondence.