Quantum Giant Magnons

TL;DR

This paper investigates quantum giant magnons within the O(N) sigma-model, employing large N analysis and Bethe Ansatz techniques, revealing their interpretation as Fermi sea holes and connecting to solvable Bose gas models.

Contribution

It provides the first exact quantum analysis of giant magnons using Bethe Ansatz and identifies a solvable limit linking to weakly-interacting Bose gases.

Findings

Quantum giant magnons can be interpreted as holes in the Fermi sea.

A solvable Bethe Ansatz limit describes a weakly-interacting Bose gas.

Connections established between O(N) model, Bose gas, and XXZ spin chain.

Abstract

The giant magnons are classical solitons of the O(N) sigma-model, which play an important role in the AdS/CFT correspondence. We study quantum giant magnons first at large N and then exactly using Bethe Ansatz, where giant magnons can be interpreted as holes in the Fermi sea. We also identify a solvable limit of Bethe Ansatz in which it describes a weakly-interacting Bose gas at zero temperature. The examples include the O(N) model at large N, weakly interacting non-linear Schrodinger model, and nearly isotropic XXZ spin chain in the magnetic field.