Finite-size Effect for Dyonic Giant Magnons in $CP^3_{\beta}$

TL;DR

This paper investigates finite-size effects on dyonic giant magnons in a deformed $ ext{AdS}_4 imes ext{CP}^3$ background, employing a classical spectral curve approach to derive dispersion relation corrections.

Contribution

It introduces a twisted algebraic curve method to compute finite-size corrections for giant magnons in the $ ext{CP}^3_{eta}$ background, confirming results obtained by different approaches.

Findings

Finite-size corrections match previous results from alternative methods.

The classical spectral curve approach is effective for deformed backgrounds.

The study confirms the universality of finite-size effects in this setting.

Abstract

We studied the finite-size giant magnons in $\text{AdS}_4\times\text{CP}^3_{\beta}$ background using the classical spectral curve constructed in this paper. We computed the finite-size corrections to the dispersion relations for the $RP^3$ giant magnons using our twisted algebraic curve based on the method proposed in arXiv:0810.1246, in which the authors computed the finite-size corrections of giant magnons in $\text{AdS}_4\times\text{CP}^3$ by introducing a finite-size resolvent $G_{\text{finite}}(x)$. We obtained exactly the same result as in arXiv:1106.3686, where a totally different approach was used.