Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM

摘要

We use generalized unitarity at the integrand-level to directly constructudlocal, manifestly dual-conformally invariant formulae for all two-loopudscattering amplitudes in planar, maximally supersymmetric Yang-Mills theoryud(SYM). This representation separates contributions into manifestly finite andudmanifestly divergent terms---in a way that renders all infrared-safeudobservables (including ratio functions) calculable without any need forudregulation. These results perfectly match the all-loop BCFW recursionudrelations, to which we provide a closed-form solution valid throughudtwo-loop-order. Finally, we describe and document a Mathematica package whichudimplements these results, available as part of this work's source files on theudarXiv.