On the Rotating and Oscillating strings in $(AdS_3\times S^3)_{\varkappa}$

TL;DR

This paper investigates rigidly rotating and oscillating strings in a $$-deformed $AdS_3 imes S^3$ background, deriving solutions and dispersion relations that connect to known results in the undeformed limit.

Contribution

It introduces new classes of rotating string solutions in the $$-deformed background and analyzes their dispersion relations, extending the understanding of string dynamics in deformed geometries.

Findings

Derived giant magnon and single spike solutions in the deformed background.

Verified dispersion relations reduce to known forms as deformation parameter approaches zero.

Explored oscillating string solutions in the deformed $S^3$ subspace.

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.