Pohlmeyer reduction and Darboux transformations in Euclidean worldsheet AdS_3

TL;DR

This paper enhances the Pohlmeyer reduction method by integrating Darboux transformations to generate diverse string solutions in Euclidean AdS_3, aiding in the study of gluon amplitudes and correlators in AdS/CFT.

Contribution

It introduces a novel combination of Pohlmeyer reduction with Darboux and Crum transformations to produce new string solutions with multiple kinks and breathers in Euclidean AdS_3.

Findings

Constructed string solutions with arbitrary kinks and breathers.

Identified dressed giant gluon as a single breather solution.

Extended the applicability of Pohlmeyer reduction in AdS/CFT contexts.

Abstract

Pohlmeyer reduction has been instrumental both in the program for computing gluon scattering amplitudes at strong coupling, and more recently in the progress towards semiclassical three-point correlators of heavy operators in AdS/CFT. After a detailed review of the method, we combine it with Darboux and Crum transformations in order to obtain a class of string solutions corresponding to an arbitrary number of kinks and breathers of the elliptic sinh-Gordon equation. We also use our construction in order to identify the previously found dressed giant gluon with the single breather solution.