On two fermion BMN operators

TL;DR

This paper analyzes the mixing and anomalous dimensions of scalar and two-fermion BMN operators in N=4 SYM, providing a method to compute two-loop corrections and exploring the role of anomalies in operator mixing.

Contribution

It introduces a method using harmonic superspace differentiation to determine two-loop anomalous dimensions of BMN operators, linking mixing with anomalies and extending loop order calculations.

Findings

Agreement with diagonalization results for low J

Derived a formula for the generalized Konishi anomaly

Resolved mixing for J=2 up to order g^2

Abstract

We show how to determine the lowest order mixing of all scalar with two-fermion two impurity BMN operators in the antisymmetric representation of SO(4). Differentiation on harmonic superspace allows one to derive two-loop anomalous dimensions of gauge invariant operators from this knowledge: the value for the second anomalous correction to the dimension is essentially the square of the two-fermion admixture. The method effectively increases the loop order by one. For low J we find agreement to all orders in N with results obtained upon diagonalisation of the N=4 dilation operator. We give a formula for the generalised Konishi anomaly and display its role in the mixing. For J=2 we resolve the mixing up to order $g^2$ in the singlet representation. The sum of the anomaly and the naive variation of the leading two-fermion admixtures to the singlets is exactly equal to the two-fermion terms in the antisymmetric descendants.