Tree-level scattering amplitudes from the amplituhedron

TL;DR

This paper explores how the amplituhedron geometry encodes tree-level scattering amplitudes in planar N=4 super Yang-Mills theory, providing a geometric approach that simplifies calculations of complex quantum interactions.

Contribution

It demonstrates how differential equations uniquely determine the amplituhedron volume for certain scattering amplitudes, advancing geometric methods in quantum field theory.

Findings

Differential equations fix the amplituhedron volume for specific amplitudes

Geometric approach simplifies high-order amplitude calculations

Provides a new perspective on scattering amplitude computation

Abstract

A central problem in quantum field theory is the computation of scattering amplitudes. However, traditional methods are impractical to calculate high order phenomenologically relevant observables. Building on a few decades of astonishing progress in developing non-standard computational techniques, it has been recently conjectured that amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. After providing an introduction to the subject at tree-level, we discuss a special class of differential equations obeyed by the corresponding volume forms. In particular, we show how they fix completely the amplituhedron volume for next-to-maximally helicity violating scattering amplitudes.