Abstract
We study rigidly rotating strings in the $\varkappa$-deformed $AdS_3 \times S^3$ background. We find out two classes of solutions corresponding to the giant magnon and single spike solutions of the string rotating in two $S^2_{\varkappa}$ subspace of rotations reduced along two different isometries. We verify that the dispersion relations reduce to the well known relation in the $\varkappa\rightarrow 0$ limit. We further study some oscillating string solutions in the $S^3_{\varkappa}$ subspace.
Highlights
JHEP09(2014)048 subsectors of the q-deformed AdS5 × S5 superstring action was studied and the classical integrable structure of anisotropic Landau-Lifshitz sigma models was derived by taking fast-moving limits in [20]
We find out two classes of solutions corresponding to the giant magnon and single spike solutions of the string rotating in two Sκ2 subspace of rotations reduced along two different isometries
The semiclassical calculations in the string theory side has shown that the multi spin rotating and pulsating string solutions beyond their BPS limit with large charges are in perfect agreement with the ones calculated in dual gauge theory
Summary
Using C1 = v, we evaluate the conserved charges using the integrals mentioned in the appendix. The difference E − Jφ remains finite and can be evaluated to be. Putting the values of sin θ1 and sin θ2 into the above equation, we can see it translates to sin. It can be proved that the conserved charges in this case obey the dispersion relation as κ2 sin(. Which is the same dispersion relation as mentioned in [40]. We can take a κ → 0 limit to get (2.47). Which is the giant magnon dispersion relation in R × S2 as mentioned in [26]
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