On the Scattering of Magnon Boundstates

TL;DR

This paper analyzes the scattering properties of magnon boundstates in the context of planar N=4 SUSY Yang-Mills, deriving exact and semiclassical S-matrices and confirming their consistency at strong coupling.

Contribution

It provides the first derivation of the boundstate S-matrix from the conjectured magnon S-matrix and compares it with semiclassical string results.

Findings

Exact S-matrix for magnon boundstates with arbitrary constituents

Analytic structure with simple and double poles

Agreement between quantum and semiclassical S-matrices at strong coupling

Abstract

We study the scattering of magnon boundstates in the spin-chain description of planar N=4 SUSY Yang-Mills. Starting from the conjectured exact S-matrix for magnons in the SU(2) sector, we calculate the corresponding S-matrix for boundstates with an arbitrary number of constituent magnons. The resulting expression has an interesting analytic structure with both simple and double poles. We also calculate the semiclassical S-matrix for the scattering of the corresponding excitations on the string worldsheet known as Dyonic Giant Magnons. We find precise agreement with the magnon boundstate S-matrix in the limit of large 't Hooft coupling.