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Zusammenfassung

We apply recently developed integrable spin chain and dilatation operator techniques in order to compute the planar one-loop anomalous dimensions for certain operators containing a large number of scalar fields in N = 4 Super Yang-Mills. The first set of operators, belonging to the SO(6) representations [J, L − 2J, J], interpolate smoothly between the BMN case of two impurities (J = 2) and the extreme case where the number of impurities equals half the total number of fields (J = L/2). The result for this particular [J, 0, J] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation. We then identify a second set of operators which also belong to [J, L− 2J, J] representations, but which do not have a BMN limit. In this case the anomalous dimension of the [J, 0, J] operator does match the Frolov-Tseytlin prediction. We also show that the fluctuation spectra for this [J, 0, J] operator is consistent with the string prediction.