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We present a calculation of the four-loop anomalous dimension of the SU(2) sector Konishi operator in N=4 SYM, as an example of wrapping corrections to the known result for long operators. We use the known dilatation operator at four loops acting on long operator, and just calculate those diagrams which are affected by the change from operator length L > 4 to L = 4. We find that the answer involves a Zeta[5], so it has trancendentality degree five. Our result differs from previous proposals and calculations. We also discuss some ideas for extending this analysis to determine finite size corrections for operators of arbitrary length in the SU(2) sector.
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
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
The spin chain formulation of the operator spectrum of the N=4 super Yang-Mills theory is haunted by the problem of ``wrapping, i.e. the inapplicability of the formalism for short spin chain length at high loop-order. The first instance of wrapping c
We show that the number of half-supersymmetric p-branes in the Type II theories compactified on orbifolds is determined by the wrapping rules recently introduced, provided that one accounts correctly for both geometric and non-geometric T-dual config
We revisit the calculation of instanton effects in correlation functions in ${cal N}=4$ SYM involving the Konishi operator and operators of twist two. Previous studies revealed that the scaling dimensions and the OPE coefficients of these operators d