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We study a general class of spinning pulsating strings in \((AdS_5 \times S^5)_{\varkappa }\) background. For these family of solitons, we examine the scaling relation between the energy, spin or angular momentum. We verify that in \(\varkappa \rightarrow 0 \) limit these relations reduce to the undeformed \(AdS_5 \times S^5\) case. We further study an example of a string which is spinning in the \(\varkappa \)-deformed \({\hbox {AdS}}_5\) and \({\hbox {S}}^5\) simultaneously and find out the scaling relation among various conserved charges.

Spinning pulsating strings in $$(AdS_5 \times S^5)_{\varkappa }$$ ( A d S 5 × S 5 ) ϰ