Operator mixing in image SYM: The Konishi anomaly re-re-visited Original Research Article

The supersymmetry transformation relating the Konishi operator to its lowest descendant in the 10 of image is not manifest in the image formulation of the theory but rather uses an equation of motion. On the classical level one finds one operator, the unintegrated chiral superpotential. In the quantum theory this term receives an admixture by a second operator, the Yang–Mills part of the Lagrangian. It has long been debated whether this “anomalous” contribution is affected by higher loop corrections. We present a first principles calculation at the second non-trivial order in perturbation theory using supersymmetric dimensional reduction as a regulator and renormalisation by Z-factors. Singular higher loop corrections to the renormalisation factor of the Yang–Mills term are required if the conformal properties of two-point functions are to be met. These singularities take the form determined in preceding work on rather general grounds. Moreover, we also find non-vanishing finite terms.