Giant Magnons under NS-NS and Melvin Fields

TL;DR

This paper studies how NS-NS and Melvin fields affect giant magnons, revealing modifications in dispersion relations and highlighting the role of spiky string profiles in these deformations.

Contribution

It provides the first detailed analysis of giant magnons under NS-NS and Melvin fields, deriving modified dispersion relations and exploring their connection to deformed spin chains.

Findings

Presence of a prefactor in the angular momentum due to fields

Corrections in the sine function of the dispersion relation

Deformed giant magnons relate to spin chain deformations

Abstract

The giant magnon is a rotating spiky string configuration which has the same dispersion relation between the energy and angular momentum as that of a spin magnon. In this paper we investigate the effects of the NS-NS and Melvin fields on the giant magnon. We first analyze the energy and angular momenta of the two-spin spiky D-string moving on the $AdS_3\times S^1$ with the NS-NS field. Due to the infinite boundary of the AdS spacetime the D-string solution will extend to infinity and it appears the divergences. After adding the counter terms we obtain the dispersion relation of the corresponding giant magnon. The result shows that there will appear a prefactor before the angular momentum, in addition to some corrections in the sine function. We also see that the spiky profile of a rotating D-string plays an important role in mapping it to a spin magnon. We next investigate the energy and angular momentum of the one-spin spiky fundamental string moving on the $R \times S^2$ with the electric or magnetic Melvin field. The dispersion relation of the corresponding deformed giant magnon is also obtained. We discuss some properties of the correction terms and their relations to the spin chain with deformations.