Finite size effect from classical strings in $AdS_3 \times S^3$ with NS-NS flux

TL;DR

This paper analyzes finite size effects of classical strings in $AdS_3 imes S^3$ with NS-NS flux, deriving exponential corrections to dispersion relations using Lambert W-functions.

Contribution

It provides explicit analytic expressions for finite size corrections of classical strings in $AdS_3 imes S^3$ with NS-NS flux, including giant magnons, single spikes, and GKP strings.

Findings

Derived exponential corrections to dispersion relations.

Expressed finite size GKP string relation analytically with Lambert W-function.

Extended understanding of string dynamics in flux backgrounds.

Abstract

We study the finite size effect of rigidly rotating strings and closed folded strings in $AdS_3\times S^3$ geometry with NS-NS B-field. We calculate the classical exponential corrections to the dispersion relation of infinite size giant magnon and single spike in terms of Lambert $\mathbf{W}-$function. We also write the analytic expression for the dispersion relation of finite size Gubser-Klebanov-Polyakov (GKP) string in the form of Lambert $\mathbf{W}-$function.