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arXiv · 1007.2356

One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory

Andre Grossardt·Jan Plefka
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Abstract

We report on a systematic study of scalar field three-point functions in planar SU(N) N=4 super Yang-Mills theory. The motivation for this work is to provide sufficient data for future conjectures on the higher-loop form of the structure constants possibly involving integrability. For this we have computed a sample of 70 structure constants at one-loop order involving primary operators of up to and including length five built entirely from scalar fields. We observe in all 17 cases occurring in our sample that the one-loop structure constant of two protected chiral primary operators and one unprotected operator is given by a simple linear function involving the anomalous scaling dimension of the latter. Moreover, a similar simple one-loop formula is proven for the three-point structure constants of the Konishi operator and two arbitrary protected or un-protected operators. It is again determined by the anomalous scaling dimensions of the operators involved.

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Andre Grossardt, Jan Plefka. 2010-07-14. One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory. https://arxiv.org/abs/1007.2356

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