Higher Loops Beyond the SU(2) Sector
Joseph A. Minahan
TL;DR
The paper extends integrability-based analyses of N=4 SYM to coherent operators in the SU(3) and SO(4) sectors, arguing these sectors can be effectively closed in the thermodynamic limit and enabling modified Bethe equations to predict anomalous dimensions. It demonstrates two-loop agreement with semiclassical string results for several rational configurations, using reductions to SU(2)×SU(2) and collective-coordinate descriptions, but finds general three-loop mismatches except at special points (notably BMN and J=L/3). The work highlights the subtle interplay between gauge theory and string theory beyond the SU(2) sector and underscores the role of 1/L mixing corrections and sector reductions in shaping higher-loop correspondences. Overall, it underscores both the promise and the limitations of extending integrability-based gauge/string comparisons to richer sub-sectors of N=4 SYM.
Abstract
We consider the case of coherent gauge invariant operators in the SU(3) and SO(4) sectors. We argue that in many cases, these sectors can be closed in the thermodynamic limit, even at higher loops. We then use a modification of the Bethe equations which is a natural generalization of a proposal put forward by Serban and Staudacher to make gauge theory predictions for the anomalous dimensions for a certain class of operators in each sector. We show that the predictions are consistent with semiclassical string predictions at two loops but in general fail to agree at three loops. Interestingly, in both cases there is one point in the configuration space where the gauge theory and string theory predictions agree. In the SU(3) case it corresponds to a circular string with R-charge assignment (J,J,J).