Color/kinematics duality for general abelian orbifolds of $ \mathcal{N} $  = 4 super Yang-Mills theory

To explore color/kinematics duality for general representations of the gauge group we formulate the duality for general abelian orbifolds of the SU( N ), $ \mathcal{N} $ = 4 super Yang-Mills theory in four dimensions, which have fields in the bi-fundamental representation, and use it to construct explicitly complete four-vector and four-scalar amplitudes at one loop. For fixed number of supercharges, graph-organized L -loop n -point integrands of all orbifold theories are given in terms of a fixed set of polynomials labeled by L representations of the orbifold group. In contrast to the standard duality-satisfying presentation of amplitudes of the $ \mathcal{N} $ = 4 super Yang-Mills theory, each graph may appear several times with different internal states. The color and R-charge flow provide a way to deform the amplitudes of orbifold theories to those of more general quiver gauge theories which do not necessarily exhibit color/kinematics duality on their own