Higher Loops Beyond the SU(2) Sector

TL;DR

This paper extends the analysis of higher-loop corrections to anomalous dimensions in SU(3) and SO(4) sectors, proposing a generalized Bethe ansatz and comparing gauge theory predictions with string theory results.

Contribution

It introduces a modified Bethe equation approach for higher loops in SU(3) and SO(4) sectors, exploring their consistency with semiclassical string theory.

Findings

Predictions match string theory at two loops.

Discrepancies appear at three loops.

A special configuration shows exact agreement.

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).