On two-fermion BMN operators

We show how to determine the lowest order mixing of all scalar with twofermion 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 g2 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.