# Tropical Grassmannians, cluster algebras and scattering amplitudes

## TL;DR

This paper introduces a cluster algebra framework to compute generalized biadjoint scalar amplitudes associated with Grassmannians, linking tropical geometry and scattering amplitudes through algebraic mutations.

## Contribution

It presents a novel cluster algebra approach to calculating scattering amplitudes related to Grassmannians, connecting tropical geometry with amplitude computations.

## Key findings

- Finite cluster algebra triangulates the tropical Grassmannian
- Amplitude volume computed via tropical Grassmannian
- Entire amplitude constructed through mutations from a single term

## Abstract

We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians ${\rm Gr}(k,n)$. A finite cluster algebra provides a natural triangulation for the tropical Grassmannian whose volume computes the scattering amplitudes. Using this method one can construct the entire colour-ordered amplitude via mutations starting from a single term.