Surprises from the Resolution of Operator Mixing in N = 4 SYM

TL;DR

This paper revisits operator mixing in N=4 SYM, providing a new method for calculating anomalous dimensions and discovering an operator with unexpectedly zero anomalous dimension at certain orders.

Contribution

It introduces a general numerical approach for resolving operator mixing and computes anomalous dimensions for specific operators, revealing surprising results.

Findings

Identified an operator with zero anomalous dimension up to order g^4.

Resolved mixing for 15 scalar singlet operators at order g^2.

Found an operator with the same one-loop anomalous dimension as the Konishi multiplet.

Abstract

We reexamine the problem of operator mixing in N = 4 SYM. Particular attention is paid to the correct definition of composite gauge invariant local operators, which is necessary for the computation of their anomalous dimensions beyond lowest order. As an application we reconsider the case of operators with naive dimension Delta_0=4, already studied in the literature. Stringent constraints from the resummation of logarithms in power behaviours are exploited and the role of the generalized N = 4 Konishi anomaly in the mixing with operators involving fermions is discussed. A general method for the explicit (numerical) resolution of the operator mixing and the computation of anomalous dimensions is proposed. We then resolve the order g^2 mixing for the 15 (purely scalar) singlet operators of naive dimension \Delta_0=6. Rather surprisingly we find one isolated operator which has a vanishing anomalous dimension up to order g^4, belonging to an apparently long multiplet. We also solve the order g^2 mixing for the 26 operators belonging to the representation 20' of SU(4). We find an operator with the same one-loop anomalous dimension as the Konishi multiplet.