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

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.

18 pages, 1 figure, typos fixed, minor changes, to appear in JHEP

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