Resurgence of the Tilted Cusp Anomalous Dimension

TL;DR

This paper employs resurgent methods to analyze the tilted cusp anomalous dimension, enabling precise interpolation between weak and strong coupling regimes using purely perturbative data.

Contribution

It introduces a novel application of resurgent extrapolation to extract non-perturbative insights from perturbative expansions of the cusp anomalous dimension.

Findings

Accurately interpolates between weak and strong coupling limits.

Identifies singularities affecting convergence of expansions.

Matches physical structure with non-perturbative data.

Abstract

We use resurgent extrapolation and continuation methods to extract detailed analytic information about the tilted cusp anomalous dimension solely from its weak coupling and strong coupling expansions. This enables accurate and smooth interpolation between the weak and strong coupling limits, and identifies the relevant singularities governing the finite radius of convergence of the weak coupling expansion and the asymptotic nature of the strong coupling expansion. The input data is purely perturbative, generated from the BES equations, and these resurgent methods extract accurate non-perturbative information which matches the underlying physical structure.