One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices

TL;DR

This paper introduces a twistor string inspired formalism for calculating one-loop MHV amplitudes in N=4 super Yang-Mills theory, simplifying their representation and connecting to previous results.

Contribution

It presents a novel off-shell formalism using MHV vertices to compute loop amplitudes, leading to a simplified and exact integral representation.

Findings

Exact evaluation of one-loop MHV amplitudes as dispersion integrals

New simplified form of MHV amplitudes matching previous results

Formalism naturally incorporates large classes of Feynman diagrams

Abstract

We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of MHV one-loop scattering amplitudes with an arbitrary number of external legs in N=4 super Yang-Mills. Remarkably, our approach naturally leads to a representation of the amplitudes as dispersion integrals, which we evaluate exactly. This yields a new, simplified form for the MHV amplitudes, which is equivalent to the expressions obtained previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.