Beyond cusp anomalous dimension from integrability in SYM$_4$

TL;DR

This paper investigates the sub-leading correction to the cusp anomalous dimension in N=4 SYM theory, analyzing its behavior at weak and strong coupling and confirming consistency with string theory predictions.

Contribution

It provides a detailed analysis of the first sub-leading correction to the cusp anomalous dimension using integrability, extending previous results beyond the leading order.

Findings

Agreement with string theory at strong coupling

Explicit integral equation for sub-leading correction

Insights into high spin expansion in N=4 SYM

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. This term is still governed by a linear integral equation which we study in the weak and strong coupling regimes. In the strong coupling regime we find agreement with the string theory computations