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.

20 pages, clarifications added, version to appear in JHEP

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• Double Wick rotating Green-Schwarz strings
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• $I$ in generalized supergravity
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
• Integrability of the eta-deformed Neumann-Rosochatius model
• On circular strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Spiky strings in $\varkappa$-deformed $AdS$
• Minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with Poincare coordinates
• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3