Magnon Bound-state Scattering in Gauge and String Theory

TL;DR

This paper investigates the scattering properties of magnon bound states in gauge and string theory, deriving conditions for bound state formation, constructing their S-matrices, and connecting their scattering phases to classical soliton interactions.

Contribution

It derives the bound state conditions, constructs their S-matrices for BDS and AFS models, and links scattering phases to classical soliton dynamics.

Findings

Bound states correspond to simple poles in the scattering matrix.

The bound state S-matrix has a richer pole structure than elementary magnons.

Large coupling limit matches semiclassical soliton scattering.

Abstract

It has been shown that, in the infinite length limit, the magnons of the gauge theory spin chain can form bound states carrying one finite and one strictly infinite R-charge. These bound states have been argued to be associated to simple poles of the multi-particle scattering matrix and to world sheet solitons carrying the same charges. Classically, they can be mapped to the solitons of the complex sine-Gordon theory. Under relatively general assumptions we derive the condition that simple poles of the two-particle scattering matrix correspond to physical bound states and construct higher bound states ``one magnon at a time''. We construct the scattering matrix of the bound states of the BDS and the AFS S-matrices. The bound state S-matrix exhibits simple and double poles and thus its analytic structure is much richer than that of the elementary magnon S-matrix. We also discuss the bound states appearing in larger sectors and their S-matrices. The large 't Hooft coupling limit of the scattering phase of the bound states in the SU(2) sector is found to agree with the semiclassical scattering of world sheet solitons. Intriguingly, the contribution of the dressing phase has an independent world sheet interpretation as the soliton-antisoliton scattering phase shift. The small momentum limit provides independent tests of these identifications.