The Resurgence of the Cusp Anomalous Dimension

TL;DR

This paper explores the resurgent properties of the cusp anomalous dimension's strong coupling expansion, revealing nonperturbative effects and proposing a transseries approach that enables unambiguous resummation and interpolation between coupling regimes.

Contribution

It introduces a transseries ansatz for the cusp anomalous dimension and analyzes its resurgence structure, connecting nonperturbative phenomena to the BES equation's analyticity conditions.

Findings

Identifies nonperturbative phenomena in both coupling directions.

Shows the transseries leads to an unambiguous resummation.

Enables strong/weak coupling interpolation.

Abstract

This work addresses the resurgent properties of the cusp anomalous dimension's strong coupling expansion, obtained from the integral Beisert-Eden-Staudacher (BES) equation. This expansion is factorially divergent, and its first nonperturbative corrections are related to the mass gap of the $O(6)$ $\sigma$-model. The factorial divergence can also be analysed from a resurgence perspective. Building on the work of Basso and Korchemsky, a transseries ansatz for the cusp anomalous dimension is proposed and the corresponding expected large-order behaviour studied. One finds non-perturbative phenomena in both the positive and negative real coupling directions, which need to be included to address the analyticity conditions coming from the BES equation. After checking the resurgence structure of the proposed transseries, it is shown that it naturally leads to an unambiguous resummation procedure, furthermore allowing for a strong/weak coupling interpolation.