Nonlocal Symmetries and Factorized Scattering

TL;DR

This paper investigates whether nonlocal Yangian symmetries can ensure factorized scattering in two-dimensional integrable models, expanding understanding beyond local charge conservation.

Contribution

It demonstrates that nonlocal Yangian symmetry can imply factorized scattering, providing new insights into integrability without relying on local higher charges.

Findings

Yangian symmetry constrains three-particle scattering processes

Nonlocal charges can underpin integrability in certain models

Results apply to su(N), u(1|1), and su(2|2) symmetries in AdS/CFT

Abstract

Conventionally, factorized scattering in two dimensions is argued to be a consequence of the conservation of local higher charges. However, integrability may well be realized via nonlocal charges, while higher local charges are not known. Here we address the question of whether a nonlocal Yangian symmetry implies factorized scattering of the S-matrix. We explicitly study the constraints on three-particle scattering processes of particles transforming in the fundamental representations of su(N), u(1|1), and the centrally extended su(2|2) underlying the dynamic scattering and hexagon form factors in AdS/CFT. These considerations shed light on the role of the Yangian as an axiomatic input for the bootstrap program for integrable theories.