Exact solutions for N-magnon scattering

TL;DR

This paper derives explicit, determinant-based formulas for N-magnon scattering states on R x S^3, facilitating the study of magnon interactions within the AdS/CFT framework.

Contribution

It introduces a novel explicit construction of N-magnon scattering solutions using the dressing method and Hirota form, expanding analytical tools in integrable models.

Findings

Explicit N-magnon scattering solutions in Hirota form

Determinant representation for multi-magnon states

Potential for developing effective magnon Hamiltonians

Abstract

Giant magnon solutions play an important role in various aspects of the AdS/CFT correspondence. We apply the dressing method to construct an explicit formula for scattering states of an arbitrary number N of magnons on R x S^3. The solution can be written in Hirota form and in terms of determinants of N x N matrices. Such a representation may prove useful for the construction of an effective particle Hamiltonian describing magnon dynamics.