Resurgence of the dressing phase for ${\rm AdS}_5\times {\rm S}^5$

TL;DR

This paper explores the resummation of the strong coupling expansion of the AdS5×S5 superstring dressing phase, revealing non-perturbative contributions that restore crossing symmetry and hint at a semiclassical origin.

Contribution

It introduces a modified Borel-Ecalle resummation incorporating non-perturbative sectors to recover the dressing phase with new exponentially suppressed terms.

Findings

Non-perturbative sectors organize into instanton-like contributions.

The summed instanton contributions satisfy crossing symmetry.

Non-perturbative terms have a semiclassical origin from the world-sheet perspective.

Abstract

We discuss the resummation of the strong coupling asymptotic expansion of the dressing phase of the ${\rm AdS}_5\times {\rm S}^5$ superstring. The dressing phase proposed by Beisert, Eden and Staudacher can be recovered from a modified Borel-Ecalle resummation of this asymptotic expansion only by completing it with new, non-perturbative and exponentially suppressed terms that can be organized into different sectors labelled by an instanton-like number. We compute the contribution to the dressing phase coming from the sum over all the instanton sectors and show that it satisfies the homogeneous crossing symmetry equation. We comment on the semiclassical origin of the non-perturbative terms from the world-sheet theory point of view even though their precise explanation remains still quite mysterious.