Abstract
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. Based on the organization of amplitudes required by the duality between color and kinematics in orbifold theories we show how the amplitudes of certain non-factorized mattercoupled supergravity theories can be found through a double-copy construction. We also carry out a comprehensive search for theories with fields solely in the adjoint representation of the gauge group and amplitudes exhibiting color/kinematics duality for all external states and find an interesting relation between supersymmetry and existence of the duality.
Highlights
Recent detailed investigations of properties of gauge theories with fields in the adjoint representation of a semi-simple Lie group have revealed that their scattering amplitudes have a surprisingly rich structure, especially in the presence of supersymmetry
We will find an interesting relation with supersymmetry: whenever pure YM theory coupled to a single fermion is supersymmetric in a given dimension D, the corresponding tree-level amplitudes obey color/kinematics duality
In this paper we discussed in detail the color/kinematics duality for general abelian orbifolds of N = 4 super Yang-Mills (sYM) theory with an unitary gauge group
Summary
Recent detailed investigations of properties of gauge theories with fields in the adjoint representation of a semi-simple Lie group have revealed that their scattering amplitudes have a surprisingly rich structure, especially in the presence of supersymmetry. These states are massless provided that the D-branes are placed at a fixed point of the action of the orbifold group; the corresponding fields transform in the bi-fundamental representation of the gauge group This construction can be realized from a field theory perspective [17, 18] by starting with maximally-supersymmetric gauge theory and projecting onto the Γ-invariant states while allowing Γ to act both on the R-symmetry and on the gauge group indices.
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