On the giant magnon and spike solutions for strings on AdS$_3\times$ S$^3$

TL;DR

This paper investigates rotating string solutions, including magnon and spike configurations, on AdS$_3$ and S$^3$ backgrounds with various deformations, revealing finite corrections and new solution types with physical interpretations.

Contribution

It introduces new rotating string solutions on deformed AdS$_3$ and S$^3$ backgrounds, analyzing their dispersion relations and physical properties.

Findings

Existence of magnon and spike solutions with magnetic fields.

Finite corrections to dispersion relations due to Melvin deformation.

Identification of circular and helical string solutions with their charge relations.

Abstract

We study solutions for the rotating strings on the sphere with a background NS-NS field and on the Anti-de-Sitter spacetime. We show the existence of magnon and single spike solutions on R$\times$S$^2$ in the presence of constant magnetic field as two limiting cases. We also study the solution for strings on AdS$_3\times$ S$^3$ with Melvin deformation. The dispersion relations among various conserved charges are shown to receive finite corrections due to the deformation parameter. We further study the rotating string on AdS$_3 \times$ S$^3$ geometry with two conserved angular momenta on S$^3$ and one spin along the AdS$_3$. We show that there exists two kinds of solutions: a circular string solution and a helical string. We find out the dispersion relation among various charges and give physical interpretation of these solutions.