  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.
