Recursive structures for the tree amplitudes of multiple gauge groups

Abstract

Recently, we enlarged the tree-level Britto-Cachazo-Feng-Witteii (BCFW) recursive relations to be applied to the product gauge theory with fermions that are bifundamentals of the product group. In this paper, we extend this recursive method to the toy model of multiple gauge theory where the gauge group is a direct product of any number of gauge groups as SU(Ni) x... x SU(AFK.) and the fermions are multifundamenals as (NI, - - - Nk.). From this models specifying the number of gauge bosons of k - 2 gauge groups, we get the maximally-helicity-violating (MHV) amplitudes of the SU(NI) x SU(N2) x U(1) gauge group.