The full strong coupling expansion of the cusp anomalous dimension

TL;DR

This paper derives the complete strong-coupling expansion of the cusp anomalous dimension in ${ m extbf{N}=4}$ super Yang--Mills theory, revealing its nonperturbative structure and resurgence pattern.

Contribution

It provides the full transseries and nonperturbative classification for the cusp anomalous dimension's strong-coupling expansion, including explicit Stokes constants.

Findings

Exact determinant ratio representation with simple expansions

Nonperturbative contributions classified by partitions into odd integers

Resurgence pattern exhibits fermionic-type behavior

Abstract

We present the full transseries of the strong-coupling expansion of the cusp anomalous dimension in ${\cal N}=4$ super Yang--Mills theory. This quantity admits an exact representation as a ratio of two determinants with particularly simple strong-coupling expansions. Nonperturbative contributions are classified by partitions into distinct non-negative odd integers and obey a universal structure. The corresponding Stokes constants are computed iteratively. The resulting resurgence pattern exhibits fermionic-type behavior.