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We compute the three-loop anomalous dimension of the BMN operators with charges J=0 (the Konishi multiplet) and J=1 in N=4 super-Yang-Mills theory. We employ a method which effectively reduces the calculation to two loops. Instead of using the superconformal primary states, we consider the ratio of the two-point functions of suitable descendants of the corresponding multiplets. Our results unambiguously select the form of the N=4 SYM dilatation operator which is compatible with BMN scaling. Thus, we provide evidence for BMN scaling at three loops.
We present a new method for computing the Konishi anomalous dimension in N=4 SYM at weak coupling. It does not rely on the conventional Feynman diagram technique and is not restricted to the planar limit. It is based on the OPE analysis of the four-p
We compute the dilatation generator in the su(2) sector of planar N=4 super Yang-Mills theory at four-loops. We use the known world-sheet scattering matrix to constrain the structure of the generator. The remaining few coefficients can be computed di
In the context of the superconformal N=4 SYM theory the Konishi anomaly can be viewed as the descendant $K_{10}$ of the Konishi multiplet in the 10 of SU(4), carrying the anomalous dimension of the multiplet. Another descendant $O_{10}$ with the same
We study cluster adjacency conjectures for amplitudes in maximally supersymmetric Yang-Mills theory. We show that the n-point one-loop NMHV ratio function satisfies Steinmann cluster adjacency. We also show that the one-loop BDS-like normalized NMHV
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