MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops

TL;DR

This paper demonstrates how one-loop MHV amplitudes in N=4 Super Yang-Mills can be derived from Wilson loops, providing a unified approach that matches known results and clarifies the structure of divergences and finite parts.

Contribution

It introduces a Wilson loop-based method to compute one-loop MHV amplitudes with arbitrary external legs in N=4 SYM, confirming known expressions and revealing new structural insights.

Findings

Derived universal function for one-loop MHV amplitudes using Wilson loops

Matched the known infinite sequence of MHV amplitudes in N=4 SYM

Reproduced four-point amplitude to all orders in epsilon

Abstract

It is a remarkable fact that MHV amplitudes in maximally supersymmetric Yang-Mills theory at arbitrary loop order can be written as the product of the tree amplitude with the same helicity configuration and a universal, helicity-blind function of the kinematic invariants. In this note we show how for one-loop MHV amplitudes with an arbitrary number of external legs this universal function can be derived using Wilson loops. Our result is in precise agreement with the known expression for the infinite sequence of MHV amplitudes in N=4 super Yang-Mills. In the four-point case, we are able to reproduce the expression of the amplitude to all orders in the dimensional regularisation parameter epsilon. This prescription disentangles cleanly infrared divergences and finite terms, and leads to an intriguing one-to-one mapping between certain Wilson loop diagrams and (finite) two-mass easy box functions.