English

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

High Energy Physics - Theory 2017-05-22 v2

Abstract

We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and divergent terms---in a way that makes manifest the exponentiation of infrared divergences at the integrand-level. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a Mathematica package which implements these results, available as part of this work's source files on the arXiv.

Keywords

Cite

@article{arxiv.1505.05886,
  title  = {Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM},
  author = {Jacob L. Bourjaily and Jaroslav Trnka},
  journal= {arXiv preprint arXiv:1505.05886},
  year   = {2017}
}

Comments

Corrections made including an important erratum: merging finite integrands does not always result in finite integrals. Language modified to reflect this fact, but implications are left to future work. 58 pages, 85 figures, and a Mathematica package (with a demonstration notebook)

R2 v1 2026-06-22T09:39:06.442Z