One-loop gauge theory amplitudes in N=4 super Yang-Mills from MHV vertices

We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in 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 Feymnan diagrams. As an example, we apply this formalism to the particular class of supersymmetric 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. (C) 2004 Elsevier B.V. All rights reserved.