Trivalent Feynman Diagrams as a Flag

Abstract

By identifying each standard flag with a trivalent Feynman diagram, the corresponding propagators can be read directly from the flag itself. Within the flag representation, the kinematic Jacobi identity (equivalently, the residue theorem on moduli spaces) admits a natural interpretation as the equivalence between a complete flag and its gapped counterpart. Using flags together with Orlik-Solomon algebras, we reconstruct the intersection numbers of twisted cocycles, thereby obtaining the bi-adjoint amplitude. Moreover, employing flag simplices enables the construction of the Z-amplitude in the alpha' -> 0 limit. By further examining pairings of specific flags, we also recover the Cachazo-He-Yuan (CHY) representation of the bi-adjoint amplitude.