A Twistor approach to one-loop amplitudes in N=1 supersymmetric Yang-Mills theory

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.