On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$

Abstract

We study rigidly rotating strings in the $\varkappa$-deformed $Ad{S}_3\times S^3$ background. We find out two classes of solutions corresponding to the giant magnon and single spike solutions of the string rotating in two $S_{\varkappa }^2$ subspace of rotations reduced along two different isometries. We verify that the dispersion relations reduce to the well known relation in the $\varkappa \to 0$ limit. We further study some oscillating string solutions in the $S_{\varkappa }^3$ subspace.

arXiv comment20 pages, clarifications added, version to appear in JHEP

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