Splitting CEGM Amplitudes

TL;DR

This paper introduces a new kinematic subspace where CEGM scattering amplitudes simplify into rational functions called simplex amplitudes, revealing new zeros and offering a novel geometric approach to amplitude derivation.

Contribution

It presents a novel kinematic subspace for CEGM amplitudes, simplifying their structure and connecting them to string integrals and tropical geometry.

Findings

CEGM amplitudes split into simple rational functions in the new subspace

Discovery of specific zeros of CEGM amplitudes

Connection between amplitude splits and tropical determinantal varieties

Abstract

The CEGM formalism offers a general framework for scattering amplitudes, which rests on Grassmannians, moduli spaces and tropical geometry. The physical implications of this generalization are still to be understood. Conventional wisdom says that key features of scattering amplitudes, like factorization at their poles into lower-point amplitudes, are associated to their singularities. The factorization behavior of CEGM amplitudes at their poles is interesting but complicated. Recent developments have revealed important properties of standard particle and string scattering amplitudes from factorizations, known as splits, that happen away from poles. In this paper we introduce a kinematic subspace on which the CEGM amplitude splits into very simple rational functions. These functions, called simplex amplitudes, arise from stringy integrals for the multivariate beta function, and also from restricting the biadjoint scalar amplitude in quantum field theory to certain kinematic loci. Using split kinematics we also discover a specific class of zeros of the CEGM amplitude. Our construction rests on viewing positive moduli space as a product of simplices, and it suggests a novel approach for deriving scattering amplitudes from tropical determinantal varieties.