Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel

TL;DR

This paper develops a new method to analyze the strong coupling expansion of $ ext{N}=4$ SYM observables, revealing a simple structure in their transseries and resurgence properties, verified through numerical analysis.

Contribution

It introduces an efficient approach to generate the full transseries for $ ext{N}=4$ SYM observables by reorganizing the determinant's transseries at large coupling.

Findings

Revealed a simple underlying structure in the transseries of the determinant.

Established a relation between exponentially suppressed corrections and perturbative series.

Verified the resurgence structure through high-precision numerical analysis.

Abstract

In this paper I continue the program of studying the strong coupling expansion of certain observables in $\mathcal{N}=4$ supersymmetric Yang--Mills theory, which are given by a determinant with a matrix Bessel kernel. I show that, by reorganizing the transseries of the determinant at large values of the 't Hooft coupling, a simple underlying structure emerges, in which each exponentially suppressed correction is related to the perturbative series in a simple way. This new approach provides an efficient method to generate the full transseries for $\mathcal{N}=4$ SYM observables, such as the cusp anomalous dimension, multi-gluon scattering amplitudes, and the octagon form factor. Using high-precision numerical analysis, I verify the results and provide a complete description of the resurgence structure of the strong coupling expansion.