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On two fermion BMN operators

Burkhard Eden
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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.

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Burkhard Eden. 2003-07-15. On two fermion BMN operators. https://doi.org/10.1016/j.nuclphysb.2003.12.036

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