On the non-planar β-deformed $\mathcal{N}=4$ super-Yang–Mills theory

The β-deformation is one of the two superconformal deformations of the 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 non-planar two-loop amplitude of this theory and show that, despite having only supersymmetry, the 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 super-Yang–Mills theory at three- and four-loop orders and points to the existence of additional structure in both the deformed and the undeformed theories.