Operator mixing in N=4 SYM: The Konishi anomaly revisited

TL;DR

This paper revisits the Konishi anomaly in N=4 SYM, analyzing operator mixing and showing that the anomaly's structure is more complex than previously thought, with implications for its loop-level exactness.

Contribution

It provides a detailed analysis of operator mixing in the Konishi anomaly, challenging the notion of one-loop exactness and extending the understanding to BMN operators.

Findings

Explicit two-loop mixing matrix calculation in supersymmetric dimensional reduction scheme.

Demonstration that the separation of classical and quantum anomaly terms is not feasible in superconformal schemes.

Clarification that the Konishi anomaly involves mixing of operators with different conformal properties.

Abstract

In the context of the superconformal N=4 SYM theory the Konishi anomaly can be viewed as the descendant $K_{10}$ of the Konishi multiplet in the 10 of SU(4), carrying the anomalous dimension of the multiplet. Another descendant $O_{10}$ with the same quantum numbers, but this time without anomalous dimension, is obtained from the protected half-BPS operator $O_{20'}$ (the stress-tensor multiplet). Both $K_{10}$ and $O_{10}$ 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 $K_{10}$ is allowed to appear in the right-hand side of the Konishi anomaly equation, the protected one $O_{10}$ 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 g^4 ("two loops") in the supersymmetric dimensional reduction scheme.