two loop amplitudes

Local integrand representations of all two-loop amplitudes in planar SYM. 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 manifestly divergent terms -- in a way that renders all infrared-safe observables (including ratio functions) calculable without any need for regulation. 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 url{arXiv:1505.05886}.


References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Golden, John; McLeod, Andrew J.: Cluster algebras and the subalgebra constructibility of the seven-particle remainder function (2019)
  2. Herrmann, Enrico; Trnka, Jaroslav: UV cancellations in gravity loop integrands (2019)
  3. Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt; Wilhelm, Matthias: Rationalizing loop integration (2018)
  4. Heslop, Paul; Tran, Vuong-Viet: Multi-particle amplitudes from the four-point correlator in planar ( \mathcalN=4) SYM (2018)
  5. Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav: Prescriptive unitarity (2017)
  6. Dennen, T.; Prlina, I.; Spradlin, M.; Stanojevic, S.; Volovich, A.: Landau singularities from the amplituhedron (2017)
  7. Rao, Junjie: Positivity, Grassmannian geometry and simplex-like structures of scattering amplitudes (2017)
  8. Badger, Simon; Mogull, Gustav; Peraro, Tiziano: Local integrands for two-loop all-plus Yang-Mills amplitudes (2016)
  9. Bern, Zvi; Herrmann, Enrico; Litsey, Sean; Stankowicz, James; Trnka, Jaroslav: Evidence for a nonplanar amplituhedron (2016)
  10. Bourjaily, Jacob L.; Franco, Sebastián; Galloni, Daniele; Wen, Congkao: Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams (2016)
  11. Bourjaily, Jacob L.; Heslop, Paul; Tran, Vuong-Viet: Amplitudes and correlators to ten loops using simple, graphical bootstraps (2016)
  12. Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia: Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory (2016)
  13. Badger, Simon; Mogull, Gustav; Ochirov, Alexander; O’Connell, Donal: A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory (2015)
  14. Bourjaily, Jacob L.; Trnka, Jaroslav: Local integrand representations of all two-loop amplitudes in planar SYM (2015)