Structure Constants of Short Operators in Planar N=4 Supersymmetric Yang-Mills Theory

We present a conjecture for the three-point functions of single-trace operators in planar N = 4 super -Yang-Mills theory at finite coupling, in the case where two operators are protected. Our proposal is based on the hexagon representation for structure constants of long operators, which we complete to incorporate operators of any length using data from the TBA-QSC formalism. We perform various tests of our conjecture, at weak and strong coupling, finding agreement with the gauge theory through 5 loops for the shortest three-point function and with string theory in the classical limit.

Automated summary

We propose a conjecture for the three-point functions of single-trace operators in planar N=4 super-Yang-Mills theory at finite coupling, specifically when two operators are protected. Our proposal is based on the hexagon representation for structure constants of long operators, which we extend to incorporate operators of arbitrary length using data from the TBA-QSC formalism. We perform various tests of our conjecture, finding agreement with the gauge theory through 5 loops for the shortest three-point function and with string theory in the classical limit.