Abstract
Basso, Komatsu and Vieira recently proposed an all-loop framework for the computation of three-point functions of single-trace operators of \( \mathcal{N}=4 \) super-Yang-Mills, the “hexagon program”. This proposal results in several remarkable predictions, including the three-point function of two protected operators with an unprotected one in the SU(2) and SL(2) sectors. Such predictions consist of an “asymptotic” part — similar in spirit to the asymptotic Bethe Ansatz of Beisert and Staudacher for two-point functions — as well as additional finite-size “wrapping” Lüscher-like corrections. The focus of this paper is on such wrapping corrections, which we compute at three-loops in the SL(2) sector. The resulting structure constants perfectly match the ones obtained in the literature from four-point correlators of protected operators.
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Eden, B., Sfondrini, A. Three-point functions in \( \mathcal{N}=4 \) SYM: the hexagon proposal at three loops. J. High Energ. Phys. 2016, 165 (2016). https://doi.org/10.1007/JHEP02(2016)165
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DOI: https://doi.org/10.1007/JHEP02(2016)165