Permutations and the Loop
Abstract
We consider the one-loop two-point function for multi-trace operators in the U(2) sector of =4 supersymmetric Yang-Mills at finite N. We derive an expression for it in terms of U(N) and Sn+1 group theory data, where n is the length of the operators. The Clebsch-Gordan operators constructed in 0711.0176, which are diagonal at tree level, only mix at one loop if you can reach the same (n+1)-box Young diagram by adding a single box to each of the n-box Young diagrams of their U(N) representations (which organise their multi-trace structure). Similar results are expected for higher loops and for other sectors of the global symmetry group.
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