Three-point functions in N=4 SYM: the hexagon proposal at three loops

Basso, Komatsu and Vieira recently proposed an all-loop framework for the computation of three-point functions of single-trace operators of 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" Ltischer-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.