Strong coupling for planar ${\cal N}=4$ SYM theory: an all-order result

TL;DR

This paper computes the all-order strong coupling behavior of the generalized scaling function in planar ${ m extbf{N}=4}$ SYM theory, linking gauge theory results with string theory predictions in a specific double scaling limit.

Contribution

It provides the first explicit all-order strong coupling computation of the generalized scaling function for high spin and large twist operators in ${ m extbf{N}=4}$ SYM, including numerical and string theory comparisons.

Findings

Excellent agreement between asymptotic gauge theory results and numerical solutions.

Numerical evaluation of non-asymptotic contributions.

Predictions consistent with string theory calculations.

Abstract

We propose a scheme for determining a generalised scaling function, namely the Sudakov factor in a peculiar double scaling limit for high spin and large twist operators belonging to the $sl(2)$ sector of planar ${\cal N}=4$ SYM. In particular, we perform explicitly the all-order computation at strong 't Hooft coupling regarding the first (contribution to the) generalised scaling function. Moreover, we compare our asymptotic results with the numerical solutions finding a very good agreement and evaluate numerically the non-asymptotic contributions. Eventually, we illustrate the agreement and prediction on the string side.