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arXiv · 0804.2923

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

Bum-Hoon Lee·Rashmi R. Nayak·Kamal L. Panigrahi·Chanyong Park
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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.

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Bum-Hoon Lee, Rashmi R. Nayak, Kamal L. Panigrahi, Chanyong Park. 2008-06-16. On the giant magnon and spike solutions for strings on AdS$_3\times$ S$^3$. https://doi.org/10.1088/1126-6708%2F2008%2F06%2F065

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