On the non-planar beta-deformed N=4 super-Yang-Mills theory

The beta-deformation is one of the two superconformal deformations of the N=4 super-Yang-Mills theory. At the planar level it shares all of its properties except for supersymmetry, which is broken to the minimal amount. The tree-level amplitudes of this theory exhibit new features which depart from the commonly assumed properties of gauge theories with fields in the adjoint representation. We analyze in detail complete one-loop amplitudes and a nonplanar two-loop amplitude of this theory and show that, despite having only N=1 supersymmetry, two-loop amplitudes have a further-improved ultraviolet behavior. This phenomenon is a counterpart of a similar improvement previously observed in the double-trace amplitude of the N=4 super-Yang-Mills theory at three and four loop order and points to the existence of additional structure in both the deformed and undeformed theories.