A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory

TL;DR

This paper extends twistor string theory methods to compute one-loop amplitudes in N=1 super Yang-Mills, providing a new simple integral representation that matches previous results for MHV amplitudes.

Contribution

It introduces a novel twistor-inspired formalism for N=1 super Yang-Mills loop amplitudes, generalizing the N=4 approach and simplifying calculations.

Findings

Derived a new dispersion integral representation for N=1 amplitudes

Calculated one-loop MHV amplitudes with arbitrary external legs

Results agree with previous cut-constructibility methods

Abstract

We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.