Grassmannian Geometry of Scattering Amplitudes

Nima Arkani-Hamed is Professor of Physics at the Institute for Advanced Study, Princeton. Jacob Bourjaily is Assistant Professor of Physics at the Niels Bohr International Academy and Discovery Center at the University of Copenhagen. Freddy Cachazo is the Gluskin Sheff Freeman Dyson Chair in Theoretical Physics at the Perimeter Institute for Theoretical Physics, Ontario. Alexander Goncharov is Professor of Mathematics at Yale University, Connecticut. Alexander Postnikov is Professor of Applied Mathematics and Algebraic Combinatorics at the Massachusetts Institute of Technology. Jaroslav Trnka is a Postdoctoral Researcher at California Institute of Technology.

Acknowledgements; 1. Introduction; 2. Introduction to on-shell functions and diagrams; 3. Permutations and scattering amplitudes; 4. From on-shell diagrams to the Grassmannian; 5. Configurations of vectors and the positive Grassmannian; 6. Body configurations, graphs, and permutations; 7. The invariant top-form and the positroid stratification; 8. (Super) conformal and dual conformal invariance; 9. Positive diffeomorphisms and Yangian invariance; 10. The kinematical support of physical on-shell forms; 11. Homological identities among Yangian-invariants; 12. (Relatively) orienting canonical coordinate charts on positroids; 13. Classification of Yangian-invariants and their relations; 14. The Yang–Braxter relation and ABJM theories; 15. On-shell diagrams for theories with N<4 supersymmetries; 16. Dual graphs and cluster algebras; 17. On-shell representations of scattering amplitudes; 18. Outlook; References.