On the Tree-Level S-Matrix of Yang-Mills Theory

TL;DR

This paper explores the computation of tree-level scattering amplitudes in Yang-Mills theory using the B-model on supertwistor space, translating Feynman diagram calculations into algebraic geometry problems.

Contribution

It demonstrates that the B-model reproduces all 6-particle amplitudes, including non-MHV configurations, and verifies key gauge theory properties for n-particle amplitudes.

Findings

Successfully reproduces all 6-particle amplitudes including non-MHV cases

Shows n-particle amplitudes obey gauge theory properties like parity and soft/collinear limits

Recasts amplitude calculations into algebraic equations solved by the B-model

Abstract

In this note we further investigate the procedure for computing tree-level amplitudes in Yang-Mills theory from connected instantons in the B-model on P^{3|4}, emphasizing that the problem of calculating Feynman diagrams is recast into the problem of finding solutions to a certain set of algebraic equations. We show that the B-model correctly reproduces all 6-particle amplitudes, including non-MHV amplitudes with three negative and three positive helicity gluons. As a further check, we also show that n-particle amplitudes obtained from the B-model obey a number of properties required of gauge theory, such as parity symmetry (which relates an integral over degree d curves to one over degree n-d-2 curves) and the soft and collinear gluon poles.