Beyond cusp anomalous dimension from integrability

TL;DR

This paper analyzes the sub-leading correction to the cusp anomalous dimension in ${ m f N}=4$ SYM theory, providing insights into weak and strong coupling regimes and confirming known results while predicting higher order terms.

Contribution

It refines the integral equation approach to study sub-leading corrections, enabling detailed analysis of weak and strong coupling behaviors and making new predictions.

Findings

Weak coupling expansion confirms four-loop results

Predictions for higher order terms at weak coupling

Agreement with string theory predictions at strong coupling

Abstract

We study the first sub-leading correction $O((\ln s)^0)$ to the cusp anomalous dimension in the high spin expansion of finite twist operators in ${\cal N}=4$ SYM theory. Since this approximation is still governed by a linear integral equation (derived already from the Bethe Ansatz equations in a previous paper), we finalise it better in order to study the weak and strong coupling regimes. In fact, we emphasise how easily the weak coupling expansion can be obtained, confirms the known four loop result and predicts the higher orders. Eventually, we pay particular attention to the strong coupling regime showing agreement and predictions in comparison with string expansion; speculations on the 'universal' part (upon subtracting the collinear anomalous dimension) are brought forward.