Resurgence of the Cusp Anomalous Dimension

TL;DR

This paper investigates the non-perturbative structure of the cusp anomalous dimension at strong coupling in planar N=4 super Yang-Mills theory, revealing how perturbative and non-perturbative parts form a resurgent transseries.

Contribution

It systematically analyzes the large order behavior of the strong coupling expansion and demonstrates the interrelation between perturbative and non-perturbative sectors using the Beisert-Eden-Staudacher equation.

Findings

Perturbative and non-perturbative parts form a resurgent transseries.

Non-perturbative corrections cancel Borel resummation ambiguities.

Large order behavior encodes non-perturbative information.

Abstract

We revisit the strong coupling limit of the cusp anomalous dimension in planar N=4 super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension receives non-perturbative corrections, and the complete strong coupling expansion should be a resurgent transseries. We reveal that the perturbative and non-perturbative parts in the transseries are closely interrelated. Solving the Beisert-Eden-Staudacher equation systematically, we analyze in detail the large order behavior in the strong coupling perturbative expansion and show that the non-perturbative information is indeed encoded there. An ambiguity of (lateral) Borel resummations of the perturbative expansion is precisely canceled by the contributions from the non-perturbative sectors,