Operator mixing in N = 4 SYM: The Konishi anomaly re-re-visited

TL;DR

This paper investigates the operator mixing and anomalous contributions in N=4 Super Yang-Mills theory, providing a detailed perturbative calculation of the Konishi anomaly at two loops using supersymmetric dimensional reduction.

Contribution

It offers a first principles two-loop calculation of the Konishi anomaly, revealing singular higher loop corrections and finite terms, using advanced integral evaluation techniques.

Findings

Singular higher loop corrections are necessary for conformal properties.

Finite non-vanishing terms are identified in the anomaly calculation.

The Laporta algorithm effectively evaluates complex four-loop correlators.

Abstract

The supersymmetry transformation relating the Konishi operator to its lowest descendant in the 10 of SU(4) is not manifest in the N=1 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. The core part of the problem is the evaluation of a four-loop two-point correlator which is accomplished by the Laporta algorithm. Apart from several examples of the T1 topology with two lines of non-integer dimension we need the first few orders in the epsilon expansion of three master integrals. The approach is self-contained in that all the necessary information can be derived from the power counting finiteness of some integrals.