Non-planar BCFW Grassmannian geometries

A bstract In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent shift, the n -point N k MHV tree-level amplitude in $$ \mathcal{N} N = 4 SYM theory is expressed as a sum over planar on-shell diagrams, corresponding canonical “dlog” forms on cells Grassmannian G + ( , ). Non-adjacent shifts naturally lead expansion of terms different set objects, which do not manifest cyclic ordering hidden Yangian symmetry amplitude. We show that these can be interpreted dlog non-planar geometries generalizing ) larger class objects live focus mainly case NMHV amplitudes discuss detail geometries. also propose alternative way calculate associated functions using intriguing between configurations geometry kinematical space.