Operator mixing in image SYM: The Konishi anomaly revisited Original Research Article

In the context of the superconformal image SYM theory the Konishi anomaly can be viewed as the descendant image of the Konishi multiplet in the 10 of image, carrying the anomalous dimension of the multiplet. Another descendant image with the same quantum numbers, but this time without anomalous dimension, is obtained from the protected half-BPS operator image (the stress-tensor multiplet). Both image and image are renormalized mixtures of the same two bare operators, one trilinear (coming from the superpotential), the other bilinear (the so-called “quantum Konishi anomaly”). Only the operator image is allowed to appear in the right-hand side of the Konishi anomaly equation, the protected one image does not match the conformal properties of the left-hand side. Thus, in a superconformal renormalization scheme the separation into “classical” and “quantum” anomaly terms is not possible, and the question whether the Konishi anomaly is one-loop exact is out of context. The same treatment applies to the operators of the BMN family, for which no analogy with the traditional axial anomaly exists. We illustrate our abstract analysis of this mixing problem by an explicit calculation of the mixing matrix at level image (“two loops”) in the supersymmetric dimensional reduction scheme.